微积分与线性代数学习指导与习题详解

图书信息

内容简介

随着知识和技术发展，数学学习更侧重概念与推理。本书立足学生基础差异，旨在以具 体形象又不失严谨的方式培养学生数学思维。本书虽定位于学习指导和习题详解，但是覆盖 完整的知识体系。知识点的讲解从具体问题和简短例题出发，配以图像，帮助学生理解抽象 理论。知识点、习题类型及内容的选取不需要掌握复杂的计算技巧，均从帮助学生整体理解 数学理论出发。

本书注重学生需求，汇总历年教学重点难点，总结教学经验，助力学生理解掌握数学知 识，培养数学思维能力。

目录

1. 微积分与线性代数学习指导与习题详解 目录
2. I Calculus
3. 1 Functions
4. 1.1 Definition of Function
5. 1.2 Operations on Functions
6. 1.3 Families of Functions
7. 2 Limit and Continuity
8. 2.1 An Informal Approach to Limits
9. 2.2 Computing Limits
10. 2.3 Limits (Rigorous Proof)
11. 2.4 Continuity
12. 3 The Derivative
13. 3.1 Tangent Line and Slope
14. 3.2 The Derivative Function
15. 3.3 Differentiability
16. 3.4 Basic Rules
17. 3.5 Chain Rule
18. 3.6 Implicit Differentiation
19. 3.7 Local Linear Approximation
20. 3.8 L'Hopital's rule
21. 4 Derivative in Graphing and Mean Value Theorem
22. 4.1 First Derivatives and Graphs
23. 4.2 Second Derivatives and Graphs
24. 4.3 Mean Value Theorem
25. 提取图中文字
26. 5 Integration
27. 5.1 Antiderivatives and Indefinite Integrals
28. 5.2 Integration by Substitution
29. 5.3 Definite Integration
30. 5.4 Fundamental Theorem of Calculus
31. II Linear Algebra
32. 6 Matrices
33. 6.1 System of Linear Equations
34. 6.2 Row Echelon Form
35. 6.3 Matrices and Matrix Operations
36. 6.4 Algebraic Rules and Matrices Inversion
37. 6.5 Partitioned Matrices and Block Multiplication
38. 7 Determinants
39. 7.1 Determinant of a Matrix
40. 7.2 Properties of Determinants
41. 7.3 Cramer's Rule and Applications of Determinants
42. 8 Vector Spaces
43. 8.1 Examples and Definition
44. 8.2 Subspaces
45. 8.3 Linear Independence
46. 8.4 Basis and Dimension
47. 8.5 Change of Basis
48. 8.6 Row Space and Column Space
49. 9 Linear Transformations
50. 9.1 Definition and Examples
51. 9.2 Matrix Representations of Linear Transformations
52. 10 Eigenvalues
53. 10.1 Eigenvalues and Eigenvectors
54. 10.2 Diagonalisation
55. 11 Orthogonality
56. 11.1 The Scalar Product in Rn
57. 11.2 Orthogonality
58. 11.3 The Gram-Schmidt Orthogonalisation Process
59. References
60. 展开全部