John Trangenstein : Math 108

• Homework (5%)
• 3 Midterms (20% each)
• Final (35%)

• Midterm 1
• Midterm 2
• Midterm 3

• Midterm 1
• Midterm 2
• Midterm 3

• Midterm 1
• Midterm 2
• Midterm 3

• write bounds on definite integrals
• write arguments to functions
• use different symbols for integration variables and variable outside integrals (e.g. in variation f parameters)
• write equations and inequalities, not just expressions (=,< or > must appear somewhere in each mathematical statement)
• put answers to exam questions in a specified place

• Chapter 1: Introduction
  Maple worksheet for direction fields, exact solutions and solution plots
  • 1.1: Direction Fields 8/27
  • 1.2: Some Solutions 8/27
  • 1.3: Classification of ODEs 8/27
• Chapter 2: First Order ODEs
  • 2.1: Integrating Factors 8/29
    Maple worksheet for integral curves, direction fields and exact solutions
  • 2.2: Separable Equations 8/29
  • 2.3: Modeling 8/29
  • 2.4: Existence and Uniqueness 9/3
  • 2.5: Critical Points 9/3
  • 2.6: Exact Equations 9/3
  • 2.7: Euler's Method 9/5
    • Maple worksheet for Euler's method
    • to run Euler's method in matlab,
      • copy Matlab function f in dy/dt=f to your machine
      • copy Matlab Euler's method for dy/dt=f to your machine
      • in matlab window, type
        t=0;u=1;n=10;h=0.1;euler
        Here t=initial time, u=initial solution, n=number of Euler steps, h=time increment
      • to solve a different ODE, change eulerfun.m
• Chapter 3: Second Order Linear Equations
  • 3.1: Homogeneous Equations with Constant Coefficients 9/5 constant coefficient ODEs and characteristic polynomials
  • 3.2: Fundamental Solutions of Linear Homogeneous Equations 9/5
  • 3.3: Linear Independence 9/10
  • 3.4: Complex Roots of the Characteristic Equation 9/10
  • 3.5: Repeated Roots 9/10
  • 3.6: Nonhomogeneous Equations 9/12 underdetermined coefficients
  • 3.7: Variation of Parameters 9/12 variation of parameters for general n't order equations
• Chapter 5: Series Solutions of Second Order Linear Equations
  • 5.1: Review of Power Series 9/17
  • 5.2,3: Series Solutions Near an Ordinary Point 9/19 Maple Commands for Plotting Series
  • 5.4: Regular Singular Points 9/24
  • 5.5: Euler Equations 9/24
  • 5.6,7: Series Solutions Near a Regular Singular Point 9/26
  • 5.8: Bessel's Equation 9/26
• Chapter 6: Laplace Transform Maple worksheet for Laplace transform
  • 6.1: Definition 10/1
  • 6.2: Initial Value Problems 10/1
  • 6.3: Step Functions 10/3
  • 6.4: Discontinous Forcing 10/3
  • 6.5: Impulse Functions 10/3
  • 6.6: Convolution 10/10
• Chapter 10: Partial Differential Equations
  • 10.1: Two-Point Boundary Value Problems 10/10
  • 10.2: Fourier Series 10/15 Maple commands for Fourier series
  • 10.3: Fourier Convergence Theorem 10/17 Wikipedia description of Gibbs phenomenon
  • 10.4: Even and Odd Functions 10/22
  • 10.5: Separation of Variables 10/29
  • to solve the heat equation in matlab (exercise 8 p 610)
    • copy Matlab commands to plot solution of heat equation to your machine
    • copy Matlab commands to define numerical grid to your machine
    • copy Matlab function to define heat equation pde to your machine
    • copy Matlab function to define heat equation initial condition to your machine
    • copy Matlab function to define heat equation boundary condition to your machine
    • in matlab window, type
      heat_run
      
    • to solve a different PDE, change heat_mesh.m, heat_pdefun.m, heat_icfun.m and/or heat_bcfun.m
• 10.6: Other Heat Conduction 10/31
• 10.7: Wave Equation 11/5, 11/7
• 10.8: Laplace's Equation 11/12