This is a student textbook covering essential topics in calculus usually taught in the early stages of science and engineering students in China. The requirements of such students have influenced its content and presentation helped in many ways by the authors' long and continuous experience of teaching mathematical methods to various degree students in Central South University. It is divided into two volumes.The first volume contains Calculus of single variable and infinite series. The second volume consists of Calculus of muhivariable with analysis geometrics and ordinary differential equations.

Volume Ⅰ

 Chapter Functions and Limits

1.1 Functions

1.2 Limits of sequence of number

1.3 Limit of functions

1.4 The operation of limits

1.5 The principle for existence of limits

1.6 Two important limist

1.7 Continuity of functions

1.8 Infinitesimal and infinity quantity, the order for infinitesimals

 Chapter 2 Derivatives and Differentials

2.1 The concepts of the derivative

2.2 The rules of derivation

2.3 Higher-order derivatives and differentials of functions

2.4 Differential skill

 Chapter 3 Mean Value Theorems and Applications of Derivatives

3.1 Mean value theorems

3.2 L'Hospital's rule

3.3 Properties of functions

3.4 Differentiation of arc and curvature

 Chapter 4 Indefinite Integrals

4.1 Concept and properties of indefinite integral

4.2 Integration by substitution

4.3 Integration by parts

4.4 Integration of a several kinds of special functions

 Chapter 5 The Definite Integral and Its Applications

5.1 Definition of definite integrals

5.2 Properties of definite integrals

5.3 The fundamental theorem of calculus

5.4 Techniques for the computation of definite integrals

5.5 Improper integrals

5.6 Applications of definite integrals

 Chapter 6 Infinite Series

6.1 Series with constant terms

6.2 Power series

6.3 Taylor's series

6.4 Fourier series

6.5 Expand a function into the sine series and cosine series

 Answers

Volume Ⅱ

 Chapter 7 Analytic Geometry in Space and Vector Algebra

7.1 Vector and their linear operations

7.2 Rectangular coordinate systems in space and components of vectors

7.3 The scalar product vector product mixed product

7.4 Planes and their equations

7.5 Straight lines in space and their equations

7.6 Surfaces and their equations

7.7 Space curves and their equations

7.8 Quadric surfaces

 Chapter 8 The Multivariable Differential Calculus and its Applications

8.1 Basic concepts of muhivariable functions

8.2 Limit and continuity for function of several variables

8.3 Partial derivatives and higher-order partial derivatives

8.4 Total differentials

8.5 Directional derivatives and the gradient

8.6 Differentiation of muhivariable composite functions

8.7 Differentiation of impliet functions

8.8 Applications of differential calculus of muhivariable functions in geometry

8.9 Extreme value problems for muhivariable functions

 Chapter 9 Multiple Integrals

9.1 Double integral

9.2 Evaluation of a double integral by iterated integration

9.3 Change of variables in a double integral

9.4 Improper double integrals

9.5 Applications of double integrals

9.6 Extensions to higher dimensions

9.7 Change of variables in a triple integral

 Chapter 10 Line Integrals and Surface Integrals

10.1 Line integrals with respect to arc lengths

10.2 Line integrals with respect to coordinates

10.3 Green's theorem, Path independence

10.4 Surface integrals with respect to surface areas

10.5 Surface integrals with respect to coordinates

10.6 The divergence theorem

10.7 Stokes theorem

 Chapter 11 Differential Equations

11.1 Differential equations and their solutions

11.2 Separable equations

11.3 Linear first-order equations

11.4 Homogeneous equations

11.5 Exact equations

11.6 Reducible second-order equations

11.7 second-0rder linear equations

 Answers