Calculus Training Course

Author: Han Zhigang, Wang Xiufen
Publisher:
Publish Date: 2004-05-01
Features: Introduction This textbook is written in accordance with the learning requirements for the "Advanced Mathematics" course in higher vocational and technical colleges as mandated by the Ministry of Education. The book is divided into nine chapters, covering topics such as functions, limits and continuity of functions, derivatives and differentials, applications of derivatives, indefinite integrals, definite integrals and their applications, ordinary differential equations, vector algebra and spatial analytical geometry, and multivariable calculus. Each chapter begins with a comprehensive introduction to the chapter and concludes with self-assessment exercises. Each section is divided into five modules: objectives, content analysis, detailed explanations of typical examples, summaries of rules and methods, and self-check questions. This textbook provides thorough explanations for the three-year "Advanced Mathematics" curriculum, truly emphasizing key points and highlighting difficulties. It offers detailed analyses of key and challenging concepts, with well-chosen examples that include both problem-solving processes and hints for approaching the solutions. The textbook features multiple solutions for single problems, a single method for multiple problems, flexible exercises, and summaries of patterns, aiming to help students achieve knowledge transfer and extension, gradually deepening their understanding. This textbook is designed to accompany the three-year "Advanced Mathematics" textbook published by Chemical Industry Press. It can also serve as a reference book for higher vocational and technical college students studying advanced mathematics, as well as a teaching resource for instructors.
Table of Contents
Chapter 1: Functions, Limits, and Continuity
Section 1: Functions
Section 2: Limits of Functions
Section 3: Operations on Limits
Section 4: Two Important Limits
Section 5: Infinitesimals and Infinites
Section 6: Continuity of Functions
Chapter 2: Derivatives and Differentials
Section 1: Concept of Derivatives
Section 2: Rules for Differentiation
Section 3: Derivatives of Implicit Functions and Parametric Equations
Section 4: Differentials of Functions
Chapter 3: Applications of Derivatives
Section 1: Mean Value Theorem and Determination of Monotonicity
Section 2: Extreme Values of Functions
Section 3: Graphing Functions
Section 4: Arc Differentials and Curvature
Section 5: L'H?pital's Rule
Chapter 4: Indefinite Integrals
Section 1: Indefinite Integrals and Their Properties
Section 2: Substitution Integration
Section 3: Integration by Parts
Chapter 5: Definite Integrals and Their Applications
Section 1: Concept of Definite Integrals
Section 2: Properties of Definite Integrals
Section 3: Newton-Leibniz Formula
Section 4: Substitution and Integration by Parts for Definite Integrals
Section 5: Improper Integrals
Section 6: Applications of Definite Integrals in Geometry
Section 7: Applications of Definite Integrals in Physics
Chapter 6: Ordinary Differential Equations
Section 1: Concept of Ordinary Differential Equations
Section 2: First-Order Differential Equations
Section 3: Applications of First-Order Differential Equations
Section 4: Second-Order Homogeneous Linear Differential Equations with Constant Coefficients
Section 5: Second-Order Non-Homogeneous Linear Differential Equations with Constant Coefficients
Chapter 7: Vector Algebra and Spatial Analytical Geometry
Section 1: Rectangular Coordinate System in Space
Section 2: Concept of Vectors
Section 3: Scalar Representation of Vectors
Section 4: Scalar and Vector Products of Vectors
Section 5: Planes and Their Equations
Section 6: Lines and Their Equations
Section 7: Common Spatial Surfaces
Chapter 8: Multivariable Calculus
Section 1: Concept, Limit, and Continuity of Multivariable Functions
Section 2: Partial Derivatives
Section 3: Partial Derivatives of Multivariable Composite Functions
Section 4: Extrema of Multivariable Functions
Section 5: Multivariable Differential Calculus
Chapter 9: Multivariable Integral Calculus
Section 1: Concept and Properties of Double Integrals
Section 2: Calculation of Double Integrals
Section 3: Triple Integrals and Their Calculation
Section 4: Line Integrals with Respect to Arc Length
Section 5: Line Integrals with Respect to Coordinates
Section 6: Green's Theorem