tailieunhanh - Advanced Mathematical Methods for Scientists and Engineers Episode 1 Part 1

Tham khảo tài liệu 'advanced mathematical methods for scientists and engineers episode 1 part 1', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Contents Anti-Copyright xxiv Preface xxv Advice to Warnings and Suggested About the Title . xxvii I Algebra 1 1 Sets and Functions 2 Sets . 2 Single Valued Functions. 4 Inverses and Multi-Valued Functions. 6 Transforming Equations. 9 Exercises. 11 Hints. 14 Solutions. 16 i 2 Vectors 22 Vectors. 22 Scalars and Vectors. 22 The Kronecker Delta and Einstein Summation Convention. 25 The Dot and Cross Product. 26 Sets of Vectors in n Dimensions. 33 Exercises. 36 Hints. 38 Solutions. 40 II Calculus 47 3 Differential Calculus 48 Limits of Functions . 48 Continuous Functions . 53 The Derivative . 56 Implicit Differentiation. 61 Maxima and Minima . 62 Mean Value Theorems. 66 Application Using Taylor s Theorem to Approximate Functions. 68 Application Finite Difference Schemes. 73 L Hospital s Rule. 75 Exercises. 81 Limits of Functions . 81 Continuous Functions . 81 The Derivative . 82 Implicit Differentiation. 84 Maxima and Minima. 84 Mean Value Theorems. 85 .