微积分和数学分析引论答案
数学分析(二)：多元微积分_南京大学中国大学mooc课后章节答案期末考试题库2023年
数学分析（二）：多元微积分_南京大学中国大学mooc课后章节答案期末考试题库2023年1.在3维欧氏空间中，向量 (1, 2, 1) 与 (4, 3, -5)之间的标准内积等于参考答案:52.空间曲线【图片】的长度为参考答案:5/33.【图片】与【图片】之间的内积等于参考答案:204.下列结论中, 正确的是参考答案:如果 f 是从平面到面的可微映射且其 Jacobi 矩阵的范数有界, 则 f 为Lipschitz 映射.5.【图片】在 (1,1) 处分别关于x, y 的偏导数为参考答案:2cos1, cos16.下列二元函数中, 不是凸函数的是参考答案:xy7.下列函数中, 不是有界变差函数的是参考答案:（在 0 处规定补充函数值为零）8.下列结论中，错误的是参考答案:平面上的零测集一定是可求面积集.9.设 A 是平面上的子集, 其特征函数是在 A 中定义为 1, 在 A 外定义为 0 的函数.则特征函数的间断点为参考答案:A 的边界点.10.下列集合中, 不是零测集的为参考答案:平面上的正方形区域 [0, 1]x[0, 1].11.将所有3行4列的实矩阵放在一起，构成的向量空间的维数等于参考答案:1212.下列结论中, 错误的是参考答案:函数 sin x 是 [-1, 1] 上的压缩映射13.下列结论中，正确的是参考答案:如果函数在某一点可微，则在这一点的偏导数都存在.14.下列问题中，不属于第二型曲线积分的是参考答案:已知物体的密度求其质量.15.在3维欧氏空间中，向量 (1, 2, 1) 叉乘 (4, 3, 5) 等于参考答案:(7, -1, -5)16.考虑平面上的环形区域【图片】, 其边界由两个圆周组成，半径小的称为内圆, 半径大的称为外圆. 则边界的诱导定向为参考答案:内圆顺时针, 外圆逆时针.17.向量场【图片】沿空间曲线【图片】从点 (1,0,1) 到 (0,1,0) 的积分等于参考答案:118.在4维欧氏空间中, 对称的二次型的全体构成了一个向量空间, 它的维数等于参考答案:1019.在4维欧氏空间中, 反对称的二次型的全体构成了一个向量空间, 它的维数等于参考答案:620.方程【图片】在(x,y)=(0,1) 附近确定了隐函数 y = f(x), 则 y'(0) 等于参考答案:-1/221.下列实数集的子集中, 是开集的为参考答案:(0, 1)。
微积分答案
International Monetary FundMoldova and the IMF Press Release:IMF Executive Board Completes Second Review Under the Extended Credit Facility and the Extended Fund Facility Arrangements with Moldova, Approves US$79 Million Disbursement April 7, 2011Country’s Policy Intentions DocumentsE-Mail Notification Subscribe or Modify your subscription Moldova: Letter of Intent, Supplementary Memorandum of Economic and Financial Policies, and Technical Memorandum of UnderstandingMarch 24, 2011M OLDOVA:L ETTER OF I N TE N TChişinău, March 24, 2011 Mr. Dominique Strauss-KahnManaging DirectorInternational Monetary Fund700 19th Street NWWashington, DC 20431 USADear Mr. Strauss-Kahn:The economic program supported by the IMF is playing a crucial role in restoring stability and rebuilding confidence in Moldova. With growth significantly exceeding projections in 2010, GDP has broadly recovered to pre-crisis levels. Inflation is under control, and the fiscal deficit has narrowed substantially. These remarkable results were achieved notwithstanding the challenges that the economy faces: fiscal adjustment and promotion of export-led growth require profound structural reforms; rising international food and fuel prices rekindle inflation pressures; job creation lags behind and unemployment still exceeds pre-crisis levels.The program is broadly on track. All quantitative performance criteria for end-September and most indicative targets for end-December 2010 were observed. However, the difficult political environment of 2010 and unforeseen technical complications have taken their toll, and several structural benchmarks under the program were delayed. In the coming period, we will move expeditiously to implement these measures, as well as the new reforms set forth in our agreement with the IMF. The 2011 fiscal budget consistent with the program objectives will be adopted as a prior action for completion of this review. In addition, we have prepared the Annual Progress Report on the implementation of our National Development Strategy and circulated it to the IMF Executive Board for information.In consideration of our strong record of program implementation, we request the completion of the second review of the program supported by the Extended Credit Facility and the Extended Fund Facility arrangements and the associated disbursement of SDR 50 million. As the Executive Board consideration of our request falls in early April 2011, we also request waivers of applicability of the relevant end-March performance criteria. The third program review, assessing performance based on end-March 2011 performance criteria and relevant structural benchmarks, is envisaged for June 2011. Moldova remains committed to improving the well-being of the population through reforms that promote sustainable growth and reduce poverty. In the period ahead, our program will focus on maintaining the targeted pace of fiscal adjustment; reining in inflation pressures; strengthening financial stability of the banking sector; restructuring the energy sector; rolling out the long-awaitededucation and other structural reforms that would support Moldova’s reorientation toward export-led growth.We believe that the policies set forth in the attached Supplementary Memorandum of Economic and Financial Policies (SMEFP) are adequate to achieve these objectives but will take any additional measures that may become appropriate for this purpose. We will consult with the IMF on the adoption of such additional measures in advance of revisions to the policies contained in the SMEFP, in accordance with the Fund’s policies on such consultation. We will provide the Fund with the information it requests for monitoring progress during program implementation. We will also consult the Fund on our economic policies after the expiration of the arrangement, in line with Fund policies on such consultations, while we have outstanding purchases in the upper credit tranches. Sincerely yours,/s/Vladimir FilatPrime MinisterofRepublicMoldovatheGovernmentof/s/ /s/NegruţaVeaceslavValeriu LazărFinanceofDeputy Prime Minister MinisterEconomyMinisterof/s/Dorin DrăguţanuGovernorNational Bank of MoldovaAttachment: Supplementary Memorandum of Economic and Financial PoliciesUnderstandingofMemorandumTechnicalS UPPLEME N TARY M EMORA N DUM OF E CO N OMIC A N D F I N A N CIAL P OLICIESMarch 24, 20111.The present document supplements and updates the Memoranda of Economic and Financial Policies (MEFPs) signed by the authorities of the Republic of Moldova on January 14, 2010 and June 30, 2010. It accounts for recent macroeconomic developments and introduces policy adjustments, as well as additional policies necessary to achieve the objectives of the program. We remain determined to meeting our commitments made previously under the program.I. M ACROECO N OMIC D EVELOPME N TS A N D O UTLOOK2.Growth outperformed expectations in 2010, and the economic expansion is set to continue. Real GDP rebounded by 6.9 percent in 2010, more than offsetting the economic contraction of 6 percent recorded in 2009. We expect the economic growth to return to its sustainable pace of 4½-5 percent in 2011 and thereafter. Expansion of domestic demand, exports, and investment are expected to drive activity in the near term, with tailwinds from trade liberalization reforms, a more favorable external environment, and improving competitiveness.3.Barring severe external shocks, disinflation should continue in 2011-12. Despite adjustment of energy tariffs, depreciation of the leu, and higher excise rates, inflation remained under control at around 8 percent in 2010, while core inflation declined below 5 percent. Under our baseline assumptions for international food and energy prices, we expect that inflation will decline further to 7½ percent in 2011 and about 5 percent by end-2012, the medium-term target set by the NBM. However, we recognize the risk that further surges in international food and energy prices and faster than expected rebound in domestic demand can temporarily push headline inflation above the projected path.4.Strong economic recovery boosted budget revenues and helped improve the fiscal position. In 2010, revenue significantly exceeded the program projections in nominal terms, but underperformed as percent of GDP, mainly due to high contribution to growth of the largely untaxed agriculture. Expenditure targets were also comfortably met, albeit largely due to under-spending of the capital budget caused by capacity constraints. As a result, the cash budget deficit narrowed to 2½ percent of GDP in 2010, far below the program target of5.4 percent of GDP.5.After a sharp drop to single digits in 2009, the external current account deficit widened in 2010 and will remain elevated in 2011. Rising demand for consumer and investment goods has pushed the current account deficit to an estimated 12¾ percent of GDP in 2010. The same demand factors, along with higher costs of energy imports, will likely propel the deficit even higher in 2011. The elevated deficit in 2011 will be largely financed by official assistance, private capital flows, and FDI. As the economy’s borrowing space is filling up quickly, we realize that further external borrowing should proceed at a more measured pace. We expect that from 2013, thanks to our exportpromotion efforts and economic recovery in trading partners, higher exports will more than offset the rise in imports, and the current account deficit would decline towards 10 percent of GDP.6.The situation in the financial sector has improved as well, with domestic credit rebounding and nonperforming loans declining. After the decline of 2009, domestic bank credit expanded by about 13 percent in 2010, and interest rates have declined. Meanwhile, the share of nonperforming loans declined to 13.3 percent, in part reflecting write-offs. Moreover, banks maintain large liquidity and capital buffers, remaining resilient to potential risks.II. R EVISED P OLICY F RAMEWORK FOR 2011-12A. Fiscal Policy7.Building on the better-than-expected fiscal outcome in 2010, the structural fiscal adjustment will stay on course in 2011-12. Our goal is to bring down the structural fiscal deficit excluding grants—the fiscal deficit adjusted for the effects of economic cycles—from 5½ percent of GDP at end-2010 through 4½ percent of GDP in 2011 to 3½ percent of GDP by 2012. This would largely rid the budget from its dependency on exceptional foreign aid and make public finances more resilient to macroeconomic risks. In this context, we will continue to contain the unaffordable public sector wage bill and low priority current spending, while strengthening revenue through selected tax policy measures and improved tax administration. Using the created fiscal space to increase infrastructure investment and provide well-targeted social assistance to the most vulnerable will allow us to achieve our broader development goals.8.As a next step, we will adopt a 2011 budget with a deficit of 1.9 percent of GDP as a prior action. We project that the budget revenue will amount to 37¾ percent of GDP in 2011, on account of continued progress in the tax administration reform, increased excise rates on tobacco and hard liquor—in line with our EU Association agenda—and updates of selected local taxes and fees. Implementation of various structural reforms, described below, will allow us to reduce current expenditure by 1½ percent of GDP to 34½ percent of GDP. At the same time, priority social assistance spending will be safeguarded, and capital expenditure will increase to 5¼ percent of GDP. We will seek to maintain the targeted structural fiscal adjustment in case the economic outlook and budget revenue deviate from our current projections.9.With immediate fiscal pressures easing, structural reforms will help contain the large public sector wage bill while creating space for poverty reduction actions. The significant optimization efforts in the education sector (¶19) will help finance the increase of teachers’ wages planned for September 2011. During 2011, other public wage restraints will remain in place as described in Law 355, as amended in October 2009. The only exception will be made for low-income auxilliary personnel in the budget sector (with salaries below MDL 1500), whose wages will be indexed by 8.5 percent on average from July 1, 2011 to alleviate the impact of higher than expected food and fuel prices and to avoid disincentives to labor market participation. Moreover, public sectoremployment will be capped at 212,000 positions by end-2011, reflecting the effects of the education reforms, while all vacant positions in excess of that level will be eliminated in 2011.10.Greater emphasis will be placed on synchronizing fiscal consolidation efforts at the central and local levels. The local governments will be granted greater control over local tax rates and fees to allow better revenue planning. In particular, by end-March 2011, we will ensure parliamentary passage of the necessary legal amendments to remove ceilings on existing local taxes and fees. This would allow the Chişinău municipality to raise at least MDL 100 million in additional revenues to finance, among other things (discussed in ¶21), its program of granting wage supplements and heating assistance in 2011. The practice of granting these payments will be discontinued at end-2011. The Ministry of Finance will verify compliance with these commitments.11.Going forward, we will continue trimming down current spending while creating sufficient space for the large public investment needs. In 2012, we aim to reduce the budget deficit further to ¾ percent of GDP, mainly through further rationalization of current spending (1 percent of GDP), sustained by structural reforms (¶¶19-22) that will commence in 2011 and bear fruit over the medium term. Ensuring sustainability of public finances in the medium term will also require implementation of the following measures:∙To reduce spending on goods and services, we will persevere with our procurement reform, assisted by the World Bank. The reform, to be phased in during 2011, will lower the budget costs by automating the bids for delivery of goods and services in the government’scentralized procurement agency.∙To improve control over budget planning and execution, we have drafted a law on public finance and accountability which will introduce a rule-based fiscal framework, enhance fiscal discipline, and improve transparency. We expect the law to be passed by Parliament by end-September 2011 and used in the preparation of the 2012 budget.∙To ensure the most effective allocation of capital expenditure, we will review the list of existing and envisaged capital projects, with a view to prioritize execution on the basis oftheir viability and economic growth potential. The review will also take into account pastexecution rates and capacity for implementation.∙To ensure implementation of the recently approved tax compliance strategy, by April 30, 2011, the State Tax Service (STS) will put in place operational plans for the strategyimplementation, including audit, collection of arrears, and taxpayer service activities(structural benchmark). In addition, by September 30, 2011, we will draft and submit toParliament legislation to allow indirect assessment of individuals’ income based on theirassets and other indicators as specified in the compliance strategy. On this basis, byDecember 31, 2011, we will prepare operational plans to strengthen audit, enforcement,outreach to, and education of high-wealth individuals regarding their tax compliance.∙We will reform the outdated mechanism for sick leave benefits. By March 31, 2011, we will amend legislation to assign the financial responsibility for the first day of sick leave to theemployee and the second day to the employer, effective July 1, 2011 (structural benchmark for end-April). Further legal amendments—to accompany the passage of the 2012 budget—will increase the number of sick leave days covered by employers to 3 in 2012, 4 in 2013, and6 in 2014.∙Early retirement privileges will be gradually phased out. By March 31, 2011, we will adopt legislation that, starting July 1, 2011, would raise the statutory retirement age of civilservants, judges, and prosecutors by six months every year until it reaches the regularretirement age (structural benchmark for end-April). This legislation will also extend the requirement to pay social contributions to all persons employed in Moldova in line withbilateral treaties. Another related piece of legislation, also to be passed by March 31, 2011,will put in place a policy of increasing the years of contribution required for full pensioneligibility from 30 to 35 years (and from 20 to 25 years for military and police personnel), by6 months every year, starting July 1, 2011.∙Building on the findings and recommendations of the recent IMF TA mission, we will implement measures to rationalize the use of health care. In particular, from January 1, 2012 we will introduce a copayment of 20 lei for primary care visits for uninsured patients, tomotivate them to enroll into the health insurance system. From January 1, 2013, we willintroduce small copayments for each doctor and hospital visit (5 lei for primary care, 10 leifor specialists, and 20 lei for hospital admissions) for all other categories of patients,including those who currently receive medical services free of charge. This policy will raise revenue and deter the use of unnecessary care, thus reducing the burden on the system. Tothis end, by end-April 2011 we will prepare an action plan detailing needed legislativechanges, technical preparations, and public information campaign.B. Monetary and Exchange Rate Policies12.The N BM’s monetary policy will be focused on achieving its end-2012 inflation objective of 5 ± 1½ percent. Given the fast economic recovery, closing output gap, and inflation pressures from rising international food and energy prices, the NBM’s monetary policy stance will gradually shift from supporting the recovery to addressing inflation risks. Specifically, it should focus on anchoring expectations—thereby countering the second-round effects from surging food and energy prices—and preventing excessive credit expansion. In this context, the NBM’s recent tightening measures—the 100 basis points hike in the policy interest rate and the increase in required reserve ratio from 8 percent to 11 percent— adequately address current inflation concerns. Further tightening should be conditional on marked acceleration of credit growth or rising inflation expectations.13.At the same time, the N BM will continue to strengthen the operational and legal aspects of its monetary policy framework. Consistent with the transition to inflation targeting, theindicative target for reserve money under the program will be discontinued after March 2011. Nevertheless, the NBM will continue to monitor money growth closely as an indicator of the state of domestic demand and sharp sustained moves may warrant policy action. In parallel, the NBM will continue to further enhance its communication, research, and forecasting capacities. As regards the legal framework, by end-September 2011, the NBM will propose amendments to the central bank law to strengthen its independence in line with the international best practice and establish appropriate mechanisms of internal control over NBM’s corporate governance.14.Alongside, the N BM’s exchange rate policies will remain consistent with program objectives. Specifically, NBM interventions in the foreign exchange market will continue to aim at smoothing erratic movements, but not resist sustained depreciation pressures. Should capital inflows exceed program projections, the NBM will accelerate the pace of reserve accumulation to ensure adequate buffers against the still high external vulnerabilities.C. Financial Sector Policy15.To strengthen financial stability, we will address the quasi-fiscal liabilities stemming from recent crisis management efforts. The Government’s decision to shield from losses the depositors of Investprivatbank (IPB) that failed in 2009 was a necessary step to avoid potential panic and deposit runs. However, paying out these deposits by means of a loan from the majority state-owned Banca de Economii (BEM) to IPB—in turn, enabled by a liquidity-providing loan from the NBM—has created a burden on BEM’s balance sheet that is now inhibiting its development. To address this problem, by end-May 2011 the Government will issue to BEM a long-term bond equal to the residual face value of BEM’s loan to IPB by either purchasing this loan or—subject to agreement of BEM’s minority shareholders—recapitalizing the bank. Meanwhile, the NBM will consider a limited extension of its loan to BEM to mitigate the attendant liquidity risk, and will work with BEM and the IPB liquidator to accelerate the sale of IPB assets. The Deposit Guarantee Fund will assume the responsibility for the net cost of the payout to IPB depositors and may introduce an extraordinary deposit insurance premium to gradually reimburse the Government for the cost of the bond issued to BEM.16.To handle future risks better, we aim to put in place the remaining elements of our contingency planning framework. Recent strengthening of the bank resolution framework and the establishment of a high-level Financial Stability Committee (FSC) were followed by signing of a memorandum of understanding (MoU) between key institutions involved in responding to financial emergencies. As a next step, we aim to put in place specific contingency plans for each MoU participant by end-June 2011. These plans will establish a contingency framework based on a clear set of instruments, division of roles, responsibilities, as well as coordination channels between the involved parties.17.Looking ahead, as credit growth picks up speed, the N BM will need to strengthen its bank supervision framework by improving data collection and reducing scope for regulatoryarbitrage. To this end, the NBM, based on best international practices, will develop a new reporting system for commercial banks allowing a more detailed analysis of financial sector data. In addition, by end-September 2011, the NBM and the National Commission for Financial Markets, with assistance from the World Bank, will explore options and make proposals to consolidate all credit institutions—including banks, leasing companies, savings and credit associations, and microfinance institutions—as well as insurance companies and pension funds under a common supervisory framework. Finally, by end-September 2011, the NBM in cooperation with the World Bank will evaluate the feasibility of establishing a public credit bureau to promote information exchange and prudent lending policies by banks.18.Despite earlier delays, measures to strengthen the debt restructuring and contract enforcement frameworks are being developed and will be implemented in the coming months. The NBM has already allowed faster reclassification of restructured loans into lower-risk categories. We will now ensure by end-September 2011 parliamentary passage of the legal amendments described in the SMEFP of June 30, 2010 (¶15), to enhance the speed and predictability of collateral execution by banks and to strengthen incentives for banks to restructure nonperforming loans (structural benchmark). Furthermore, with technical assistance from the World Bank and in consultation with the IMF staff, we will seek to strengthen and simplify other aspects of the insolvency framework. Specific draft legal amendments in this area will be adopted by the Government by March 2012.D. Structural ReformsRaising Efficiency of the Public Sector19.In the coming months, we will roll out the comprehensive reform of the oversized education sector. Its main goals are to eliminate excess capacity, create a leaner and better-equipped education system with adequately trained and paid staff, and provide education that meets demands of the modern economy. The reform will seek class, school, and employment consolidation. A large part of the eventual budget savings and financial assistance from the World Bank will be used to improve school quality, secure transportation for students, and repair school bus routes. Nevertheless, the reform will save about 0.5 percent of GDP on a net permanent basis from 2013 on. Our reform strategy is based on the following elements:∙Class size optimization. By September 1, 2012, we will increase class size to 30-35 students in large schools and 25-30 students in the rest. For this purpose, we will pass legalamendments to eliminate the existing norms prescribed in the Law on Education by end-July 2011. This would reduce the number of teaching positions by 1,736, including 390 positions in 2011, and lead to estimated annual savings of about MDL 94 million.∙Optimization of the school network. Gradual consolidation of the school network through closure of schools with low enrollment and securing transportation of students to nearby“hub” schools will commence this year. Its full implementation during 2011-13 would reducethe number of teaching and non-teaching positions by 2,661 and 1,426 respectively and, when completed, will generate savings of about MDL 136 million a year. We will aim to limit the attendant transportation costs to MDL 61 million per year, and will seek grant assistance from the international financial community to defray this cost.∙Reduction of non-teaching personnel and vacant positions. As a first step, we will immediately freeze hiring of non-teaching staff and eliminate 2,400 vacant positions in thesector. Alongside, we will include in the budget law for 2011 a provision establishing wage bill ceiling for education sector, resulting in all rayons reducing personnel in educationinstitutions on average by 5 percent from their level of end 2010 (5,300 positions nationwide) before academic year 2011/12. These measures would provide savings of MDL 175 million on a full-year basis.∙Increasing flexibility of labor relations in the sector. Local authorities also need support and more flexibility to be able to consolidate schools and classes. By end-July 2011, we willadopt legal amendments to the Labor Code and other enabling legislation to (i) make fixed-term (one year) contracts mandatory for teachers beyond retirement age; and (ii) allow school principals’ hiring and dismissal decisions to be based on business need and performancerather than tenure. Estimated annual savings from this measure amount to MDL 48 million. ∙Rollout of a per-student financing system. Following successful implementation of per-student financing in the pilot rayons of Cauşeni and Rişcani, the system will be expandedstarting January 1, 2012 to 9 additional rayons, as well as municipalities of Chişinău andBalţi. The system will create strong incentives to optimize schools’ financial performance. Its nationwide implementation will take place in 2013.∙Putting social protection costs in education on a means-tested basis. By end-June 2011, in consultation with the World Bank and other partners, we will conduct a thorough review ofall social expenditure in the education budget (scholarships, dormitory assistance, schoolmeals, etc.) to explore options for better targeting of such assistance to the most vulnerablegroups.In consultation with the World Bank, the Government will develop and, by end-March 2011, adopt a detailed action plan to implement this reform.20.We will reform the civil service in a way that increases efficiency without destabilizing the fiscal position. To this end, we have developed descriptions of new job functions and responsibilities for staff in central government administration along with a merit- and performance-based wage system for civil servants. Implementation of this reform will start in October 2011, and will ensure that the reform does not affect the aggregate public sector wage bill as a ratio to GDP. 21.As regards the energy sector, we will strive to achieve a stable framework for payments of current bills, pending a comprehensive sector restructuring strategy to be finalized and implemented in cooperation with the World Bank and other partners. To ensure a stablefunctioning of the sector, the Ministry of Economy, the Chişinău municipality authorities, and the key participants in the energy sector will seek to negotiate in good faith a MoU with the following key elements: (i) a monthly schedule of payments to energy suppliers that is consistent with typical collection lags in Termocom’s receivables during the heating season, (ii) full repayment of current arrears by Termocom before the following heating season; (iii) a mechanism for covering the cash gap arising from collection lags in Termocom or a bank guarantee from the Chişinău municipality backing Termocom’s adherence to the agreed payment schedule; (iv) creditors’ commitment to abstain from blocking bank accounts as long as the MoU is observed. In this context, the Chişinău municipality will budget for and pay in full its remaining debt to Termocom of MDL 64 million by end-March 2011.22.Meanwhile, we will adopt a number of legal and regulatory amendments which would help ensure cost recovery in the heating sector. By end-August 2011, we will adopt the necessary legal and/or regulatory amendments to raise the heating fee for apartments disconnected from central heating from 5 percent to 20 percent of the average heating bill. This increase is in line with regional practices and would mostly affect consumers with relatively high incomes. At the same time, the Ministry of Regional Development and Construction, the Chişinău municipality, Termocom, and the water distributor Apă Canal will seek to put an end to persistent losses caused by under-billing for hot and cold water delivery; other municipalities will seek to resolve this issue as well. And to facilitate timely collection of heating bills, by end-August 2011, we will adopt the necessary legal and/or regulatory amendments introducing a minimum payment of 40 percent of the monthly bill and setting August 1 as the deadline for settling all heating bills for the past heating season.23.With the international investment climate gradually improving, the government will accelerate the efforts to divest its noncore assets. In the first half of 2011 the government, with assistance from IFC, will put in place an advisor to review various options for private sector participation in Moldtelecom. At the same time, by mid-2011, the government will expand the list of state assets subject to privatization. This will pave the way for privatization of other large public companies. By end-September 2011, the government will approach various international financial institutions, seeking an advisor to explore options to divest Air Moldova as soon as possible. Also by end-September 2011, we shall develop a roadmap for the privatization of Banca de Economii, and, if need be, resume the engagement of the privatization advisor.Improving the Business Environment and Removing Barriers for Trade24.The wheat export ban introduced in response to dwindling grain stocks in early 2011 will be abolished as soon as possible, and we will not introduce any new barriers to trade. We plan to abolish this ban by end-April 2011, provided that domestic and regional grain shortages are alleviated. Moreover, we shall refrain from introducing any new tariff or non-tariff barriers to exports. In addition, by end-May 2011 we will conduct an assessment of the existing tariff and non-tariff barriers to trade and their consistency with Moldova’s WTO commitments with regard to market access, and will develop roadmap for their gradual elimination.。
数学分析课后习题答案
数学分析课后习题答案数学分析课后习题答案数学分析是大学数学的重要分支之一，它研究的是数学函数的性质、极限、连续性、可导性等等。
在学习数学分析的过程中，课后习题是巩固和拓展知识的重要途径。
然而，有时候我们会遇到一些难题，不知道如何下手。
为了帮助大家更好地学习数学分析，本文将提供一些常见习题的答案和解析。
一、极限与连续性1. 求极限：lim(x→0) (sinx/x)。
解析：利用极限的性质，我们可以得到lim(x→0) (sinx/x) = 1。
这是因为当x趋近于0时，sinx/x的值趋近于1。
2. 证明函数f(x) = x^2在点x = 3处连续。
解析：要证明函数f(x) = x^2在点x = 3处连续，我们需要证明lim(x→3) f(x) = f(3)。
根据函数的定义，f(3) = 3^2 = 9。
而lim(x→3) f(x) = lim(x→3) x^2 = 3^2 = 9。
因此，函数f(x) = x^2在点x = 3处连续。
二、导数与微分1. 求函数f(x) = x^3的导数。
解析：根据导数的定义，导数f'(x) = lim(h→0) (f(x+h) - f(x))/h。
对于函数f(x) = x^3，我们可以得到f'(x) = lim(h→0) ((x+h)^3 - x^3)/h。
化简后，我们得到f'(x) = 3x^2。
2. 求函数f(x) = sinx的微分。
解析：微分的定义是df(x) = f'(x)dx。
对于函数f(x) = sinx，我们已经知道它的导数f'(x) = cosx。
因此，函数f(x) = sinx的微分为df(x) = cosxdx。
三、积分与级数1. 求函数f(x) = x^2在区间[0,1]上的定积分。
解析：根据定积分的定义，函数f(x) = x^2在区间[0,1]上的定积分为∫[0,1] x^2 dx。
计算这个积分，我们得到∫[0,1] x^2 dx = [x^3/3]0^1 = 1/3。
《微积分》各章习题及详细答案之欧阳道创编
第一章 函数极限与连续一、填空题1、已知x x f cos 1)2(sin +=，则=)(cos x f 。
2、=-+→∞)1()34(lim22x x x x 。
3、0→x 时，x x sin tan -是x 的阶无穷小。
4、01sin lim 0=→xx k x 成立的k 为。
5、=-∞→x e x x arctan lim 。
6、⎩⎨⎧≤+>+=0,0,1)(x b x x e x f x 在0=x 处连续，则=b 。
7、=+→xx x 6)13ln(lim 0。
8、设)(x f 的定义域是]1,0[，则)(ln x f 的定义域是__________。
9、函数)2ln(1++=x y 的反函数为_________。
10、设a 是非零常数，则________)(lim =-+∞→xx ax a x 。
11、已知当0→x 时，1)1(312-+ax 与1cos -x 是等价无穷小，则常数________=a 。
12、函数xxx f +=13arcsin)(的定义域是__________。
13、lim ____________x →+∞=。
14、设8)2(lim =-+∞→x x ax a x ，则=a ________。
15、)2)(1(lim n n n n n -++++∞→=____________。
二、选择题1、设)(),(x g x f 是],[l l -上的偶函数，)(x h 是],[l l -上的奇函数，则中所给的函数必为奇函数。
（Ａ）)()(x g x f +；（Ｂ）)()(x h x f +；（C ）)]()()[(x h x g x f +；（D ）)()()(x h x g x f 。
2、xx x +-=11)(α，31)(x x -=β，则当1→x 时有。
（Ａ）α是比β高阶的无穷小； （Ｂ）α是比β低阶的无穷小；（C ）α与β是同阶无穷小； （D ）βα~。
数学分析与微积分的关系
数学分析与微积分的关系
数学分析和微积分是学界最重要的一类基础课程，它们有一定的联系。
本文将探讨数学分析和微积分之间的关系，并回答“它们之间有什么关系”的问题。
数学分析是一个抽象的学科，致力于研究和分析数学问题。
数学分析包括函数分析，解析几何，算子理论和拓扑学等多种研究方法。
其目的是发现数学结构的内在联系，提供有用的应用。
例如，函数分析可以用来研究波或振动，解析几何可以用来分析形状，算子理论可以用来研究系统的变化，拓扑学可以用来分析形状的不变性。
微积分是一个推理矿学科，其它基础是数学分析。
它的目标是研究函数的极限，微分，积分和变换，利用这些方法，可以推出复杂的数学模型。
微积分是数学分析的一个应用，但它也为研究数学结构、求解复杂数学问题和发现有用的应用提供了重要的有力工具。
因此，我们可以总结出数学分析和微积分之间的主要联系是：数学分析是研究并分析数学问题的抽象学科，而微积分是数学分析的一个应用，它利用数学分析的方法，推出了复杂的数学模型，为许多研究领域带来了重要的贡献。
总之，数学分析和微积分之间存在着重要的关系，数学分析是微积分的基础，而微积分又利用数学分析的方法推出了许多有用的应用。
它们的关系是相互依存的，数学分析和微积分的研究在当今的数学研究中扮演着重要的角色，有助于发展数学科学，推动各种应用的发展，为人类的社会发展做出了贡献。
以上就是数学分析与微积分的关系的研究结果。
希望经过以上研究后，读者对数学分析和微积分之间的联系有了更深刻的理解，能够更加准确地把握这两门学科之间的关系，为人类的社会发展做出自己的贡献。
微积分详解习题答案
微积分详解习题答案微积分是数学中的一门重要学科，它研究的是函数的变化规律与性质。
在学习微积分的过程中，习题是不可或缺的一部分。
通过解答习题，我们可以更好地理解微积分的概念和原理。
本文将详解一些微积分习题的答案，帮助读者更好地掌握微积分知识。
首先，让我们来看一个简单的求导题目。
假设有一个函数f(x) = 3x^2 + 2x + 1，我们需要求出它的导数。
根据求导的定义，我们可以逐项对函数中的每一项进行求导。
对于3x^2，我们可以应用求导法则，得到它的导数为6x；对于2x，它的导数为2；对于常数1，它的导数为0。
因此，函数f(x)的导数为f'(x) = 6x+ 2。
接下来，我们来看一个求定积分的例子。
假设我们需要计算函数g(x) = x^2在区间[0, 2]上的定积分。
根据定积分的定义，我们可以将区间[0, 2]划分成无限小的小矩形，然后将这些小矩形的面积相加，即可得到定积分的值。
在本例中，我们可以将区间[0, 2]划分成无限小的宽度为Δx的矩形，然后将这些矩形的面积相加。
每个矩形的面积可以用函数g(x)在该点的函数值乘以Δx来表示。
因此，定积分的值可以表示为lim(Δx→0)∑(g(xi)Δx)，其中∑表示求和，xi表示每个小矩形的中点。
通过计算，我们可以得到定积分的值为∫[0, 2]x^2dx =[x^3/3]0^2 = 8/3。
除了求导和定积分，微积分还涉及到一些其他的概念，比如极限和微分方程。
下面我们来看一个关于极限的习题。
假设有一个函数h(x) = (x^2 - 1)/(x - 1)，我们需要求出它在x趋近于1时的极限。
当x趋近于1时，函数h(x)的分子和分母都会趋近于0。
我们可以应用洛必达法则来求解这个极限。
根据洛必达法则，我们可以对函数h(x)的分子和分母同时求导，然后再求极限。
对于函数h(x)的分子，它的导数为2x；对于函数h(x)的分母，它的导数为1。
因此，在x趋近于1时，函数h(x)的极限可以表示为lim(x→1)(2x) / 1 = 2。
高三微积分习题与答案
高三微积分习题与答案高三微积分习题与答案高三是学生们备战高考的关键一年，而微积分作为数学的重要组成部分，对于理科生来说尤为重要。
在高三学习微积分的过程中，做习题是必不可少的一环。
本文将为大家提供一些高三微积分习题及其答案，希望能对同学们的学习有所帮助。
1. 求函数f(x) = 2x^3 - 5x^2 + 3x - 2的导函数f'(x)。
答案：f'(x) = 6x^2 - 10x + 3解析：对于多项式函数，求导的方法是将指数降一，然后乘以原指数的系数。
根据这个规则，我们可以得到f'(x) = 2 * 3x^(3-1) - 5 * 2x^(2-1) + 3 * 1x^(1-1)= 6x^2 - 10x + 3。
2. 求函数f(x) = e^x * sin(x)的导函数f'(x)。
答案：f'(x) = e^x * sin(x) + e^x * cos(x)解析：根据乘法法则，我们可以将f(x) = e^x * sin(x)拆分为两个函数的乘积：f(x) = u(x) * v(x)，其中u(x) = e^x，v(x) = sin(x)。
然后，根据乘法法则和指数函数的导数规则，我们可以得到f'(x) = u'(x) * v(x) + u(x) * v'(x) = e^x * sin(x) + e^x *cos(x)。
3. 求函数f(x) = ln(x^2 + 1)的导函数f'(x)。
答案：f'(x) = (2x) / (x^2 + 1)解析：根据链式法则，我们可以将f(x) = ln(x^2 + 1)拆分为两个函数的复合：f(x) = u(v(x))，其中u(x) = ln(x)，v(x) = x^2 + 1。
然后，根据链式法则和对数函数的导数规则，我们可以得到f'(x) = u'(v(x)) * v'(x) = (1 / v(x)) * v'(x) = (1 / (x^2 + 1))* (2x) = (2x) / (x^2 + 1)。
实用文档之《微积分》各章习题及详细答案
实用文档之"第一章 函数极限与连续"一、填空题1、已知x x f cos 1)2(sin +=，则=)(cos x f 。
2、=-+→∞)1()34(lim22x x x x 。
3、0→x 时，x x sin tan -是x 的 阶无穷小。
4、01sin lim 0=→xx kx 成立的k 为 。
5、=-∞→x e xx arctan lim 。
6、⎩⎨⎧≤+>+=0,0,1)(x b x x e x f x 在0=x 处连续，则=b 。
7、=+→xx x 6)13ln(lim 0 。
8、设)(x f 的定义域是]1,0[，则)(ln x f 的定义域是__________。
9、函数)2ln(1++=x y 的反函数为_________。
10、设a 是非零常数，则________)(lim =-+∞→xx ax a x 。
11、已知当0→x 时，1)1(312-+ax 与1cos -x 是等价无穷小，则常数________=a 。
12、函数xxx f +=13arcsin )(的定义域是__________。
13、lim ____________x →+∞=。
14、设8)2(lim =-+∞→xx ax a x ，则=a ________。
15、)2)(1(lim n n n n n -++++∞→=____________。
二、选择题 1、设)(),(x g x f 是],[l l -上的偶函数，)(x h 是],[l l -上的奇函数，则 中所给的函数必为奇函数。
（Ａ）)()(x g x f +；（Ｂ）)()(x h x f +；（C ）)]()()[(x h x g x f +；（D ）)()()(x h x g x f 。
2、xxx +-=11)(α，31)(x x -=β，则当1→x 时有 。
（Ａ）α是比β高阶的无穷小； （Ｂ）α是比β低阶的无穷小； （C ）α与β是同阶无穷小； （D ）βα~。
微积分(下)习题解答(第七章)
微积分（下）习题解答（第七章）综合练习71.填空题：（1）令un1(某)某n某2n22nu(某)2n22n21时级数收敛，，则limn1，故某某nu(某)n1时级数发散，故所求收敛半径为1．111n（2）因为，利用d某C某,某1，可得23某1某(3某)n011某n某d某CC,1，从而，n1(3某)23某33n01n某n1n1,某(3,3)．2(3某)n13（3）因为级数(an1an)收敛，故其部分和数列Snan1a1极限存在，所n1以极限liman存在．n（4）an收敛，且an0，故由级数收敛的必要条件知，liman0，从而，n1n11lim，故级数必发散．nan1ann（5）an(某1)n12n=an[(某1)]在某2条件收敛，故an收敛，an发2nn1n1n1散，即anyn的收敛半径为R1，由(某1)21，解得0某2，且在n1某0，某2时级数an(某1)2n收敛，故所求收敛域为[0,2]．n1（6）令un1(某)102n(2某3)2n1，则limun1(某)102(2某3)2，故nu(某)n102(2某3)21时级数收敛，102(2某3)21时级数发散，所求收敛域为：3131(,)．220220（7）limun1(某)an1313lim某2某1，故所求收敛半径为3．nu(某)na2nnn1nnn1n某n11（8）某某某某某n某e某e某1,n1n!n1n!n1n!n1(n1)!n1n!某(,)．1n1（9）某的收敛域为[1,1)，n某n的收敛域为(2,2)，且容易计算幂n2nlnnn22级数(n211n)某n的收敛半径为1，故由幂级数收敛域的性质知，nlnn2(n211n)某n的收敛域为[1,1)．nlnn21n（10）由已知limnp(e1)an1，有limn(e1)ane11，从而1，又limnn111p1()nnn1n1nanlim1，由条件an收敛，利用正项级数的比较判别法，知p的取n1p1n1()n值范围是p2．f(3)(0)2．某的系数是（11）令f(某)in某co某，将之展开成某的幂级数时，3!33(1)n某2n(1)n（12）因为co某，某(,)，令某1，从而有co1.(2n)!n0n0(2n)!2.选择题：（1）对于un(1)，易知(u2n1u2n)=0收敛，但是un(1)n发散，nn1n1n1且lim(1)0，故（A）（C）均不正确，又对任意一个收敛级数un，nnn1均有加括号的新级数(u2n1u2n)收敛，故（D）不对，因此，正确答案n1为（B）．00)1000，lim（2）若un收敛，则limun0，而lim(un1n1nn100故（B）0，nunu1(D)错误．令un2，则un收敛，但是n1发散，故（A）也是错误nn1n1un的，因此，正确选项为（C），100+un仅仅是收敛级数前添加一项，对级n1数的收敛性没有影响．（3）（A）选项是典型的莱布尼茨型交错级数，且是条件收敛的．（B）（D）选项是绝对收敛级数．（C）是发散级数，因为级数的一般项不趋于0．故选择（A）．（4）(1)(1co)(1)2in，而级数2in2是收敛的（利用n2n2nn1n1n1nn21正项级数的比较判别法：与2比较即可），故(1)n(1co)是绝对收nn1n1n敛的，所以选择（C）．（5）若级数an(某2)在某2处收敛，则由阿贝尔定理，知an(某2)n 在nn1n1故选项（D）正确，且an(某2)n的收敛半径R4，某24处绝对收敛，n1故选项（B）也正确．若级数an(某2)n在某2处条件收敛，则该级数n1的收敛半径为4（因为若收敛半径大于4，由阿贝尔定理可得an(某2)n在n1某2处绝对收敛，则为矛盾），故选项（A）也正确．若级数an(某2)nn1在某2处条件收敛，即级数an1n(某2)n在某2处发散，故有an1n(22)4an发散，从而an(某2)n在某6处敛散性不确定，nnn1n1故选项（C）说法错误．综上，本题答案选择（C）．in某2nnd某in某d某1co2in（6）因为0，又2in2收敛，01某0n2n2nn1所以利用正项级数的比较判别法知，n1n0in某d某是绝对收敛的，故选择1某（C）．（7）因为011212收敛，利用收(an2)，又an以及22nn1nn1n2an敛级数的性质及正项级数的比较判别法，知(1)nn1ann2是绝对收敛的，故选择（C）．inn(1)ninn(1)n（8）易知级数与均收敛，故级数(2)收敛．另2nnnnn1n1n1inn11inn(1)n111一方面，2，而级数()0222nnnnnnnnn1inn(1)n是发散的（利用收敛级数的性质），故(2)是条件收敛的，nnn1所以选择（B）．（9）an条件收敛，故有liman0，从而M0，使得anM，nN．又n1n所以利用正项级数的比较判别法及收敛级数anbnMbn且bn绝对收敛，n1的性质，知anbn是绝对收敛的，故选择（C）．n1un1un12(1)n1（10）对于2，lim故选项（A）(C)错误．对于，1，lim2nnununnn1nn1不存在（分奇偶子列讨论），故选项（B）错误．只有选项（B）正确．（11）若级数un与vn都发散，则(unvn)必发散．若不然，因为n1n1n10un,vnunvn，由比较判别法，得到un与vn都绝对收敛，此n1n1为矛盾，故选择（C）．（12）若幂级数an(某1)在某1处条件收敛，由Abel定理，知an(某1)nnn1n1的收敛半径为R2，故an(某1)n在(1,3)中的每一点绝对收敛，从而n1级数an绝对收敛，正确答案为（C）．n1（13）对于(1)nlnn1n11，令un，则un0且单调减少趋于零，但因为nn11lim(1)ln0，故(1)nln发散，因此（A）错误．对于交错级数nnnn111111n=，虽然满足且(1)u(1)un收敛，但u0nn22323232n1n1n是{un}非单调减少数列，即莱布尼兹判别法仅是交错级数收敛的充分条件而11非必要条件，因此（B）错误．对于(1ln)，令un，则un0且单nnn111调减少趋于零，但是级数(1ln)发散（可以利用比较判别法：与比nn1n1n较），故（D）错误．利用结论：若级数an绝对收敛，则级数an必收2n1n1敛，可知选项（C）正确．（14）对于选项（A），用反证法，设(1)un前n项部分和为Sn，假设u2nnn1n1与u2n1均收敛，则加括号后的新级数(u2n1u2n)也收敛，从而其前n 项n1n1部分和nS2nS(n)，又u2n10，故S2n1S2nu2n1S。
数学分析习题课讲义解答
16.2 级数求和计算 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
17 高维空间的点集与基本定理
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18 多元函数的极限与连续
55
19 偏导数与全微分
56
பைடு நூலகம்
20 隐函数存在定理与隐函数求导
13 数项级数
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14 函数项级数与幂级数
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15 Fourier 级数
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16 无穷级数的应用
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16.1 积分计算 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5 参考题 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5 连续函数
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5.1 连续性的概念 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Mathematical analysis exercises class lectures Answer
数学分析习题课讲义 解答
Don’t give up, never give up.
目录
1 引论
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1.1 几个常用的不等式 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
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微积分和数学分析引论答案【篇一：高数参考书】（国内教材大同小异）1高等数学第Ⅱ卷:一元微积分和微分方程，居余马等著，清华大学出版社2高等数学／西安交通大学高等数学教研室编．—2版．—北京：高等教育出版社，1986.23高等数学引论／华罗庚著．—北京：科学出版社，1984.7习题集1高等数学附册学习辅导和习题选解（同济五版）（注意：不是“高等数学习题全解指南”这本！）6 微积分／（美）m.r.施皮格尔=murray r. spiegel著；施建兵等译．—北京：科学出版社，20024，344页；30cm．—（全美经典学习指导系列）数学史和其他1古今数学思想／(美)克莱因著．—上海：上海科学技术出版社，1981.74 一个数学家的自白／(英)g. h. 哈代著；李泳评注＝a mathematicians apology．—长沙：湖南科学技术出版社，2007网站网易公开课维基百科【篇二：学习数学分析的一些建议和书籍】本帖最后由 ke.xigui 于 2009-5-21 21:49 编辑首先，只是觉得这篇东西写得很好，对学习数学分析的人可能有帮助，所以粘上来。
希望作者莫见怪。
旧版网站里许多有用的东西，但是现在找不到了，实在很可惜。
数学专业参考书整理推荐学数学要多看书，但是初学者很难知道那些书好，我从网上收集并结合自己的经验进行了整理：从数学分析开始讲起：数学分析是数学系最重要的一门课，经常一个点就会引申出今后的一门课，并且是今后数学系大部分课程的基础。
也是初学时比较难的一门课，这里的难主要是对数学分析思想和方法的不适应，其实随着课程的深入会一点点容易起来。
当大四考研复习再看时会感觉轻松许多。
数学系的数学分析讲三个学期共计15学分270学时。
将《数学分析》中较难的一部分删去再加上常微分方程的一些最简单的内容就是中国非数学专业的《高等数学》，或者叫数学一的高数部分。
记住以下几点：1，对于数学分析的学习，勤奋永远比天分重要。
2，学数学分析不难，难得是长期坚持做题和不遗余力的博览群书。
3，别指望第一遍就能记住和掌握什么，请看第二遍，第三遍，…,第阿列夫遍。
4，看得懂的仔细看，看不懂的硬着头皮看。
5，课本一个字一个字的看完，至少再看一本参考书，尽量做一本习题集。
6，开始前三遍，一本书看三遍效果好于三本书看一遍；第四遍开始相反。
7，经常回头看看自己走过的路以上几点请在学其他课程时参考。
数学分析书：初学从中选一本教材，一本参考书就基本够了。
我强烈推荐11，推荐1，2，7，8。
另外建议看一下当不了教材的16，20。
中国人自己写的：1《数学分析》陈传璋，金福临，朱学炎，欧阳光中著（新版作者顺序颠倒）应该是来自辛钦的《数学分析简明教程》，是数学系用的时间最长，用的最多的书，大部分学校考研分析的指定教材。
我大一用第二版，现在出了第三版，但是里面仍有一些印刷错误，不过克可以一眼看出来。
网络上可以找到课后习题的参考答案，不过建议自己做。
不少经济类工科类学校也用这一本书。
里面个别地方讲的比较难懂，而且比其他书少了一俩个知识点，比如好像没有讲斯托尔滋(stolz)定理，实数的定义也不清楚。
不过仍然不失为一本好书。
能广泛被使用一定有它自己的一些优势。
2《数学分析》华东师范大学数学系著师范类使用最多的书，课后习题编排的不错，也是考研用的比较多的一本书。
课本最后讲了一些流形上的微积分。
虽然是师范类的书，难度比上一本有一些降低，不过还是值得一看的。
3《数学分析》陈纪修等著以上三本是考研用的最多的三本书。
4《数学分析》李成章，黄玉民是南开大学一个系列里的数学分析分册，这套教材里的各本都经常被用到，总体还是不错的，是为教学改革后课时数减少后的数学系各门课编写的教材。
5《数学分析讲义》刘玉链我的数学分析老师推荐的一本书，不过我没有看，最近应该出了新版，貌似是第五？版，最初是一本函授教材，写的应该比较详细易懂。
不要因为是函授教材就看不起，事实上最初的函授工作都是由最好的教授做的。
细说就远了，总之可以看看。
6《数学分析》曹之江等著内蒙古大学数理基地的教材，偏重于物理的实现，会打一个很好的基础，不会盲目的向n维扩展。
适合初学者。
国家精品课程的课本。
7《数学分析新讲》张筑生公认是一本新观点的书，课后没有习题。
材料的处理相当新颖。
作者已经去世。
8《数学分析教程》常庚哲，史济怀著中国科学技术大学教材，课后习题极难。
9《数学分析》徐森林著和上面一本同出一门，清华大学教材。
程度好的同学可以试着看一看。
书很厚，看起来很慢。
10《数学分析简明教程》邓东翱著也是一本可以经常看到的书，作者已经去世。
国家精品课程的课本。
11许绍浦《数学分析教程》南京大学出版社这些书应该够了，其他书不一一列举。
从中选择一本当作课本就可以了。
外国数学分析教材：11《微积分学教程》菲赫金格尔茨著数学分析第一名著，不要被它的大部头吓到。
我大四上半年开始看，发现写的非常清楚，看起来很快的。
强烈推荐大家看一下，哪怕买了收藏。
买书不建议看价格，而要看书好不好。
一本好的教科书能打下坚实的基础，影响今后的学习。
12《数学分析原理》菲赫金格尔茨著上本书的简写，不提倡看，要看就看上本。
13《数学分析》卓立奇观点很新，最近几年很流行，不过似乎没有必要。
14《数学分析简明教程》辛钦课后没有习题，但是推荐了《吉米多维奇数学分析习题集》里的相应习题。
但是随着习题集的更新，题已经对不上号了，不过辛钦的文笔还是不错的。
15《数学分析讲义》阿黑波夫等著莫斯科大学的讲义，不过是一本讲义，看着极为吃力，不过用来过知识点不错。
16《数学分析八讲》辛钦大师就是大师，强烈推荐。
17《数学分析原理》rudin中国的数学是从前苏联学来的，和俄罗斯教材比较像，看俄罗斯的书不会很吃力。
不过这本美国的书还是值得一看的。
写的简单明了，可以自己试着把上面的定理推导一遍。
18《微积分和分析引论》库朗又一本美国的经典数学分析书。
有人认为观点已经不流行了，但是数学分析是一门基础课目的是打下一个好的基础。
19《流形上的微积分》斯皮瓦克分析的进一步。
中国的数学分析一般不讲流形上的微积分，不过流形上的微积分是一种潮流，还是看一看的好。
20《在南开大学的演讲》陈省身从中会有一些领悟，不过可惜好像网络上流传的版本少了一些内容。
21华罗庚《高等数学引论》科学出版社数学分析习题集不做题就如同没有学过一样。
希望将课本后的习题一道道自己做完，不要看答案。
买习题集也要买习题集，不买习题集的答案。
1《吉米多维奇数学分析习题集》最近几年人们人云亦云的说这本书多么不好，批评计算题数目过多，不适合数学系等等。
但这本习题集不再被广泛使用的原因是那本习题解答的出现，学生对答案的抄袭使这部书失去了价值。
如果你不看答案的话它依然是数学分析第一习题集。
不要没有做过就盲目的批评。
有没有做过自己心里知道，并会影响自己今后的学习。
2《数学分析习题课教材》第一版或《数学分析解题指南》第二版，林源渠，方企勤等两本书一样的，再版换了名字。
第一版网上有电子版，第二版可以买纸版。
和3成一套。
3《数学分析习题集》林源渠，方企勤等由于《吉米多维奇数学分析习题集》答案的出现使这本书得到的评价变高了，原因是这本书没有答案。
只能自己做。
4《数学分析习题精解》科学出版社版，还有裴礼文或者钱吉林的书过测试不错，要学数学分析不提倡。
5各种教材的答案书一堆垃圾。
毁人不倦。
【篇三：数学系书籍推荐】目录引言一数学分析二高等数学三高等代数四线性代数五分析几何六概率论七常微分方程八偏微分方程九数学物理方程(数学物理方法)十复变函数十一实变函数十二泛函分析十三高等几何十四微分几何十五拓扑学十六近世代数十七离散数学十八组合数学十九数值分析二十数学建模二十一数学史附录数学软件后记3楼引言些有经验的学长推荐些好书，以便不走弯路。
二来恰好笔者也有类似经历，初接触高等数学方面的书籍时，也不知有啥好坏或者稂莠之别，后来在一些这些书的内容中了解到、在网上一些学长的贴子中看到很多“经典”和比较“好”的教材、参考书、课外书籍等，于是在广泛查阅、拜读之后，把我所看过的和所知道的一些很好的书目记录下来，提供朋友们参考。
希望能给大家有所帮助。
实际上所谓的“好书”和经典书，并不限于数学方面，其他学科方面的有，相信大家也看过不少，这里只说数学方面的。
以下结合本人经验和一些学长的见解，共写有二十一个专题，每个专题都有该学科的简介或者是小结；相应的介绍书籍则是按【教材】、【习题集】、【辅导书】、【提高】四个方面来写，而且每本书后有简评供参考。
最后附录介绍几个常用数学软件。
============注：1)打引号或书名号的课程名词被认为是指书籍或课程名，否则是指这一数学学科类(领域)。
2)以下推荐的书籍一般不标注版本，因为随时有新版出版的可能，并且不一定新版就比旧版的好一些，有时还不如旧版的。
最好多结合几个版本来看（有三个以上版本的不要看第一版，结合看最新版和倒数几个旧版），这样能学到更多。
这是笔者的经验。
如果书后标有版本号的，一般是指比较好的版本。
3)关于出版社的问题，这个不必要过多追究，因为大部分书不会用一个以上的出版社出版，况且不同出版社出版同一本书，只是版式和符号的样式不同而已，内容不会有别。
4)书比较多，不可能每本(或者选取大多数自己喜欢的)都买，除非你非常有钱，或者是个数学书籍收藏家。
要知道，大学及其以上的教材、教参等都很贵，动辄每本二三十以上，四五十的也不少。
因此，“少而精”地买到正版的就行，其余的可以到大学图书馆借阅(大部分我都是借阅的，我可买不起^-^)。
5)由于书籍很多，本人阅历也很有限，难以面面俱到，除了【教材】外以下只为《数学分析》、《高等数学》、《高等代数》、《线性代数》、《分析几何》、《概率论》、《常微分方程》提供【习题集】、【辅导书】和【提高】，而剩下课程的相关书籍只是不完全含有以上版块。
大家可以根据相应课本寻找对应课后习题分析的参考书，或是配套的习题集即可。
4楼一、“数学分析”“数学分析”是数学或计算专业最重要的一门课，而且是今后数学专业大部分课程的基础，经常从一个知识点就能引申出今后的一门课，同时它也是初学时比较难的一门课。
这里的“难”主要是指对数学分析思想和方法的不适应（高等数学上的方法和初等数学的方法有很大不同），其实随着学习的深入，适应了方法后，会感觉一点一点地容易起来，比如当大四考研复习再看时会感觉轻松许多。
数学系的数学分析讲三个学期(各个院校应该一样吧)，学的时间也够长的~本课程主要讲的是以集合为基础而发展起来的变量和函数中的数学规律、分析和计算，是通往高等数学领域的基础工具之一。
这么多年来，国内外出现了很多非常优秀的教材和习题集以及辅导书，而且很多高校一直使用着。