Mathematical Methods

Mathematical Methods provides an introduction to vector calculus, ordinary differential equations, and partial differential equations including a variety of applications. Topics include: optimization, line and surface integrals, Green’s theorem, Stokes’ theorem, the Divergence theorem, and the theory of systems of linear differential equations.

Mathematics

Tác giả: Pamini Thangarajah
Nhà xuất bản: Mount Royal University
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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1: Power Series
1 E: Chapter Exercises
1.1: Power Series
1.1E: Exercises
1.2: Properties of Power Series
1.2E: Exercises
1.3: Taylor and Maclaurin Series
1.3E: Exercises
1.4: Working with Taylor Series
1.4E: Exercises
2: Ordinary differential equations
2.1: Linear Second Order Homogeneous Equations
2.1E: Exercises
2.2: Linear Second Order Constant Coefficient Homogeneous Equations
2.2E: Exercises
2.3: Linear Second Order Nonhomogeneous Linear Equations
2.3E: Exercises
2.4: The Method of Undetermined Coefficient
2.4E: Exercises
2E: Exercises
3: Series Solutions of Linear Second order Equations
3.1: Review of Power Series
3.1E: Exercises
3.2: Series Solutions Near an Ordinary Point I
3.2E: Exercises
3.3: Series Solutions Near an Ordinary Point II
3.3E: Exercises
3.4: Regular Singular Points: Euler Equations
3.4E: Exercises
3.5: The Method of Frobenius I
3.5E: Exercises
3.6: The Method of Frobenius II
3.6E: Exercises
3.7: The Method of Frobenius III
3.7E: Exercises
4: Linear Systems of Ordinary Differential Equations (LSODE)
4.1: Introduction to Systems of Differential Equations
4.1E: Exercises
4.2: Linear Systems of Differential Equations
4.2E: Exercises
4.3: Basic Theory of Homogeneous Linear System
4.3E: Exercises
4.4: Constant Coefficient Homogeneous Systems I
4.4E: Exercises
4.5: Constant Coefficient Homogeneous Systems II
4.5E: Exercises
4.6: Constant Coefficient Homogeneous Systems III
4.6E: Exercises
4.7: Variation of Parameters for Nonhomogeneous Linear Systems
4.7E: Exercises
5: Vector-Valued Functions
5.1: Vector-Valued Functions and Space Curves
5.1E:
5.2: Calculus of Vector-Valued Functions
5.2E:
5.3: Arc Length and Curvature
5.3E: Exercises
5.4: Motion in Space
5.4E:Exercises
5E: Excercises
6: Differentiation of Functions of Several Variables
6.1: Functions of Several Variables
6.1E:
6.2: Limits and Continuity
6.2E:
6.3: Partial Derivatives
6.3E:
6.4: Tangent Planes and Linear Approximations
6.4E:Exercises
6.5: The Chain Rule for Multivariable Functions
6.5E: Exercises
6.6: Directional Derivatives and the Gradient
6.6E: Exercises
Minima Problems
6.7E:
6.8: Lagrange Multipliers
6.8E:
6E: Chapter Review Excersies
7: Multiple Integration
7.1 :Double Integrals over Rectangular Regions
7.1E: Exercises
7.2: Double Integrals over General Regions
7.2E: Exercises
7.3: Double Integrals in Polar Coordinates
7.3E:
7.4: Triple Integrals
7.4E:
7.5: Triple Integrals in Cylindrical and Spherical Coordinates
7.5E:
7.6: Calculating Centers of Mass and Moments of Inertia
7.6E
7.7: Change of Variables in Multiple Integrals
7.7E:
7E: Chapter Review Excersies
8: Partial Differential Equations
8.1: Laplace Equations
8.2: The heat equation
8.3: Wave Equations
8E: Excercise
9: Vector Calculus
9.1: Vector Fields
9.1E: Exercises
9.2: Line Integrals
9.2E: Exercises
9.3: Conservative vector Fields
9.3E: EXERCISES
9.4: Green's Theorem
9.4E: EXERCISES
9.5: Divergence and Curl
9.5E: EXERCISES
9.6: Surface Integrals
9.6E: Exercises
9.7: Stoke's Theorem
9.7E: EXERCISES
9.8: The Divergence Theorem
9.8E: Exercises
9E: Chapter Exercises
Summary Tables
3-D Coordinate Systems
Summary of Convergence Tests
Summary of Theorems
Summary table of derivatives
Summary Table Of Integrals