本套教材是根据《工科类本科数学基础课程教学基本要求》编写的，适合高等院校工科类各专业学生使用.本套教材共12章，分上、下册.本书为下册，内容包括向量代数与空间解析几何、多元函数微分法及其应用、重积分、曲线积分与曲面积分、无穷级数，共五章.根据学生的学习规律，本套教材每章都有知识点总结，以便学生更好地掌握.作为立体化教材，本套教材配备了相应的网络学习内容.用户通过扫描书中的二维码，即可获得这些学习资源.本套教材内容丰富，简明易懂，可作为高等院校工科类各专业的大学数学教材，也可作为相关专业领域读者的参考书.

《高等数学练习册（上）》为《高等数学（上）》（孙小华、吕莉芳主编，科学出版社出版）的配套练习册，共分5章，章节的划分与《高等数学（上）》完全一致，每章按节设置练习题，包括单项选择题、填空题、判断题、计算题、证明题等题型，每章后还配有一套自测题。《高等数学练习册（上）》可作为高等职业院校、高等专科学校、普通本科院校学生学习高等数学课程的辅导教材，也可作为专升本人员复习备考的辅导教材。

本书系统而全面地介绍复变理论及其在工程问题上的应用，理论与实际应用密切结合，对工程类学科的学生来说，这种方式更生动地表达了数学理论的内涵。

《初等数论》在吸收已有初等数论教材清晰、简明、严谨的特色基础上，在内容呈现方式及论证思路方面进行了周密的准备，力求还原数学家门的思考过程，力求讲清楚所有概念、方法、定理的来龙去脉。全书有以下特点：（1）所有的定理、性质、方法及结论都不直接呈现，而是通过例题引出；（2）对于定理或性质的证明，均通过具体实例引出；（3）对一些难点内容，均提前进行了铺垫或分散处理；（4）对于新概念、新方法，均是在例题、实例等感性材料后提出；（5）全书思路清晰、简明移动，没有繁冗、复杂的论述；（6）所选的习题、例题均为有代表性的、基础的，没有涉及难题、怪题、偏题。

多元统计分析方法是处理多维数据不可或缺的重要工具，特别是随着计算机技术的发展，多元统计分析迅速发展成为统计学中一个非常重要的分支。《实用多元统计分析》在介绍多元统计分析方法的同时结合统计软件R，将理论与实际应用相结合。《实用多元统计分析》共10章，主要包括多元统计分析基础、多元正态分析、单个总体参数的检验、多个正态总体参数的比较、线性回归模型、主成分分析、因子分析、典型相关分析、判别分析、聚类分析等内容。《实用多元统计分析》可作为数学系本科生教材和工科、医科、管理、经济、教育类等专业的研究生教材使用，也可作为研究工作者或统计工作者的参考用书。

思维导图是一种思维的工具，将我们的思维过程展现在一张白纸上。它能很好地运用左右脑机能，开发大脑潜能。《思维导图玩转数学》利用思维导图的特点，帮助学生全面把握数学学科知识点和知识结构，建立知识点联系，通过复盘和错题，找出不熟的知识点，找出误区盲区，达到快速提分的效果，同时使得学习不再枯燥。

《非线性演化方程介绍非线性演化方程的物理北京、研究方法和取得的一些*新的结果，包括一些*新的结果。*后还介绍了无穷维动力系统。非线性演化方程内容非常丰富，《非线性演化方程（英）》分五章，基本还是属于介绍性的，读者可以从中对这一研究领域有一个较好的了解。

本书的编写主要有以下特点： 1. 教材编写形式新颖。每章都包括案例引出、概念分析、应用举例等内容。 2. 数学基础理论、数学建模和数学实验有机地结合。本书最后两章分别是数学建模和数学实验。 3. 以实例引出数学概念，注重数学思想方法的教学。本书以现实、生动的实例引出数学概念，使学生深入地理解数学概念产生的背景，不仅增强了学生对数学概念的认识和兴趣，而且有利于学生创新思维的发展。 4. 通过“案例”教学凸显专业特色。本书从内容的选择、例题的确立以及数学模型的建立，都力求体现专业特色；在内容编排上，以“面向专业，为专业服务”为原则，精选各专业必需的数学基础知识。 5. 教材可根据不同专业灵活选择相应的章节学习。本套书分上下两册，授课教师可根据课时数量和不同专业灵活选择相应的章节学习。

Fractional order calculus is the theory of arbitrary order differential and integral， it is unified with the integer order differential and integral calcu-lus， is the development of classical calculus， fractional calculus as a descrip-tion of classical physics and related discipline theory analytic mathematical tools have been widely accepted， but when people study complex systems and complex phenomena， the classical integer order differential and integral equation description for the systems will encounter a series of problems，therefore， there is an urgent looking forward to having a kind of mathema-tical tools available and can be based on the basic principle of the complex system modeling. Fractional-order differential equations are very suitable for describing materials and processes with memory and heritability， and their description of complex systems has the advantages of simple model-ing， clear physical meaning of parameters and accurate description.In recent decades， fractional differential equations have been increasing-ly used to describe problems in optical and thermal systems， theological and material and mechanical systems， signal processing and system identi-fication， control and robotics and their applications. Fractional differentialequations have been investigated by more and more scholars from around the world. With the emergence of fractional-order differential equation model in more and more scientific fields， the theoretical analysis of fractional-order differential equations is particularly urgent.The first chapter is mainly about some definitions， lemmas and prepa-ration theorems， preparing for the presentation of follow-up results.In chapter 2， after a brief introduction， in section 2， nonlinear frac-tional differential equations involving different Riemann-Liouville fractional derivatives are presented; in sections 3 and 4， three-point boundary value problem and multi-point boundary value problem under different conditions are discussed; in section 5， integral boundary value problem for nonlinear fractional differential equations on an unbounded domain is presented; sec-tion 6 is about the existence and uniqueness of positive solutions to arbitrary order nonlinear fractional differential equations with advanced arguments.Section 7 is concerned with the eigenvalue interval for the existence and nonexistence of at least one positive solution of nonlinear fractional dif-ferential equation with integral boundary conditions. In section 8， under certain nonlinear growth conditions of the nonlinearity， the existence of so-lutions for a nonlinear Hadamard type fractional differential equation with strip condition and p-Laplacian operator is studied.In section 9， the unique-ness， existence and nonexistence of solutions of the fractional turbulent fiow model are discussed.Chapter 3 is about nonlinear fractional integro-differential equation.Section 2 is about initial value problem for nonlinear neutral fractional integro-differential equation with nonlinear term depending on lower order derivative. In the third section， the existence of minimal nonnegative so-lution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces is discussed. Section 4 is concerned with the existence of solutions for nonlinear fractional differential equations of Volterra type with nonlocal fractional integro-differential boundary con-ditions on an infinite interval. In section 5， a Hadamard type fractional integro-differential equation on infinite intervals is considered.Nonlinear impulsive fractional differential equation is the focus of Chap-ter 4.Nonlinear impulsive fractional differential equations with anti-periodic boundary conditions are discussed in section 2. Section 3 is about nonlinear impulsive fractional differential equations with nonlocal integral boundary condition. Section 4 is concerned with nonlinear Langevin equa-tion with two different fractional orders and impulses.Chapter 5 is devoted to the system of nonlinear fractional differentialequation. In Section 2， the existence results and the monotone iterativetechnique for systems of nonlinear fractional differential equations are p-resented.Section 3 is about the existence of an extremal solution for a nonlinear system involving the right-handed Riemann-Liouville fractional derivative with nonlocal coupled integral boundary conditions. Section 4 is about the existence of solutions for a coupled system of nonlinear neutral fractional differential equations， which involves Riemann-Liouville deriva-tives of different fractional orders.Section 5 in the chapter is concerned with a coupled system of nonlinear fractional differential equations with multi-point fractional boundary conditions on an unbounded domain.At the end of each chapter， there are short notes and remarks indicating the source of the content.

本书是《微积分》（下册）的教学参考书，内容包括定积分、多元函数微积分学、无穷级数、常微分方程与差分方程等知识。全书分为三大部分，其中第一部分为对应教材的课后习题全解和总复习题全解 ；第二部分为试题选编；第三部分为试题选编全解。