3 credits
Blue Book Description: First- and second-order equations; numerical methods; special functions; Laplace transform solutions; higher order equations. Students who have passed MATH 251 may not schedule this course for credit.
Pre-requisites: MATH 141
Pre-requisite for: MATH 412, MATH 419
Bachelor of Arts: Quantification
Suggested Textbook:
William F. Trench. Elementary Differential Equations with Boundary Value Problems
Faculty Authored and Edited Books & CDs, vol. 9, Trinity University, 2013.
This book is open source and approved by the American Institute of Mathematics under their Open Textbook Initiative.
Check with your instructor to make sure this is the textbook used for your section.
Topics:
- Chapter 1: Introduction
- Section 1.2: First Order Equations
- Section 1.3: Direction Fields for First Order Equations
- Chapter 2: First Order Equations
- Section 2.1: Linear First Order Equations
- Section 2.2: Separable Equations
- Section 2.3: Existence and Uniqueness of Solutions of Nonlinear Equations
- Section 2.5: Exact Equations
- Section 2.6: Integrating Factors
- Chapter 4: Applications of First Order Equations
- Section 4.1: Growth and Decay
- Section 4.2: Cooling and Mixing
- Section 4.3: Elementary Mechanics
- Chapter 5: Linear Second Order Equations
- Section 5.1: Homogeneous Linear Equations
- Section 5.2: Constant Coefficient Homogeneous Equations
- Section 5.3: Nonhomogeneous Linear Equations
- Section 5.4: The Method of Undetermined Coefficients I
- Section 5.5: The Method of Undetermined Coefficients II
- Section 5.6: Reduction of Order
- Section 5.7: Variation of Parameters
- Chapter 6: Applications of Linear Second Order Equations
- Section 6.1: Spring Problems I
- Section 6.2: Spring Problems II
- Section 6.3: The RLC Circuit (optional)
- Section 6.3: Motion Under a Central Force (optional)
- Chapter 7: Series Solutions of Linear Second Order Equations
- Section 7.1: Review of Power Series
- Section 7.2: Series Solutions Near an Ordinary Point I
- Section 7.3: Series Solutions Near an Ordinary Point II
- Section 7.4: Regular Singular Points, Euler Equations (optional)
- Chapter 8: Laplace Transforms
- Section 8.1: Introduction to the Laplace Transform
- Section 8.2: The Inverse Laplace Transform
- Section 8.3: Solution of Initial Value Problems
- Section 8.4: The Unit Step Function
- Section 8.5: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
- Section 8.6: Convolution
- Section 8.7: Constant Coefficient Equations with Impulses
- Chapter 9: Linear Higher Order Equations (optional)
- Section 9.1: Introduction to Linear Higher Order Equations
- Section 9.2: Higher Order Constant Coefficient Homogeneous Equations
- Section 9.3: Undetermined Coefficients for Higher Order Equations
- Section 9.4: Variation of Parameters for Higher Order Equations
- Chapter 10: Linear Systems of Differential Equations (optional)
- Section 10.1: Introduction to Systems of Differential Equations
- Section 10.2: Linear Systems of Differential Equations
- Section 10.3: Basic Theory of Homogeneous Linear Systems
- Section 10.4: Constant Coefficient Homogeneous Systems I
- Section 10.5: Constant Coefficient Homogeneous Systems II
- Section 10.6: Constant Coefficient Homogeneous Systems III
- Section 10.7: Variation of Parameters for Nonhomogeneous Linear Systems