# |
Learning Outcomes |
1 |
Students will be able to classify and to identify different types of differential equations. |
2 |
Students will be able to explicitly solve several important classes of ordinary differential equations and to interpret their qualitative behaviour. |
3 |
Students will be able to apply ideas from linear algebra in order to solve single linear ordinary differential equations and systems of such equations. |
4 |
Students will be able to model certain physical phenomena using differential equations and to reinterpret their solutions physically. |
5 |
Students will be able to use power series methods to solve second order linear differential equations. |
6 |
Students will be able to apply the Laplace transform for solving differential equations. |
7 |
Students will be able to use the method of separation of variables in order to solve some basic partial differential equations via Fourier series. |
# |
Subjects |
Teaching Methods and Technics |
1 |
I. Introduction
1.1 Some Basic Mathematical Models; Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations |
lecturing, discussing, problem solving |
2 |
II. First Order Differential Equations
2.1 Linear Equations; Methods of Integrating Factors
2.2 Separable Equations, Homogeneous Equations
2.6 Exact Equations and Integrating Factors
2.8 The Existence and Uniqueness Theorem |
lecturing, discussing, problem solving |
3 |
2.4 Differences Between Linear and Nonlinear Equations
2.5 Autonomous Equations and Population Dynamics
2.7 Numerical Approximations: Euler’s Method |
lecturing, discussing, problem solving |
4 |
III. Second Order Linear Equations
3.1 Homogeneous Equations with Constant Coefficients
3.2 Fundamental Solutions of Linear Homogeneous Equations; the Wronskian
3.3 Complex Roots of the Characteristic Equation |
lecturing, discussing, problem solving |
5 |
3.4 Repeated Roots; Reduction of Order
3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients |
lecturing, discussing, problem solving |
6 |
3.6 Variation of Parameters
3.7 Mechanical and Electrical Vibrations
3.8 Forced Vibrations |
lecturing, discussing, problem solving |
7 |
IV. Higher Order Linear Equations
4.1 General Theory of nth Order Linear Equations
4.2 Homogeneous Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients |
lecturing, discussing, problem solving |
8 |
V. Series Solutions of Differential Equations
5.2 Series Solution Near an Ordinary Point Part I
5.3 Series Solution Near an Ordinary Point Part II
5.4 Euler Equation, Regular Singular Points |
lecturing, discussing, problem solving |
9 |
5.5 Series Solution Near a Regular Singular Point I
5.6 Series Solution Near a Regular Singular Point II |
lecturing, discussing, problem solving |
10 |
VI. The Laplace Transform
6.1 Definition of the Laplace Transform
6.2 Solution of Initial Value Problems
6.3 Step Functions |
lecturing, discussing, problem solving |
11 |
6.4 Differential Equations with Discontinuous Forcing Functions
6.5 Impulse Functions
6.6 The Convolution Integral
VII. Systems of Linear Equations
7.4 Basic Theory of Systems of First Order Linear Equations |
lecturing, discussing, problem solving |
12 |
7.5 Homogeneous Linear Systems with Constant Coefficients
7.6 Complex Eigenvalues
7.7 Fundamental Matrices |
lecturing, discussing, problem solving |
13 |
7.8 Repeated Eigenvalues
7.9 Nonhomogeneous Linear Systems
X. Partial Differential Equations and Fourier Series
10.1 Two-point Boundary Value Problems |
lecturing, discussing, problem solving |
14 |
10.2 Fourier series
10.3 The Fourier Convergence Theorem
10.4 Even and Odd Functions
10.5 Separation of Variables; Heat Conduction in a Rod |
lecturing, discussing, problem solving |
15 |
|
|
16 |
Final Exam |
|
# |
Learning Outcomes |
Program Outcomes |
Method of Assessment |
1 |
Students will be able to classify and to identify different types of differential equations. |
1͵11 |
1͵2 |
2 |
Students will be able to explicitly solve several important classes of ordinary differential equations and to interpret their qualitative behaviour. |
1͵11 |
1͵2 |
3 |
Students will be able to apply ideas from linear algebra in order to solve single linear ordinary differential equations and systems of such equations. |
1͵11 |
1͵2 |
4 |
Students will be able to model certain physical phenomena using differential equations and to reinterpret their solutions physically. |
1͵11 |
1͵2 |
5 |
Students will be able to use power series methods to solve second order linear differential equations. |
1͵11 |
1͵2 |
6 |
Students will be able to apply the Laplace transform for solving differential equations. |
1͵11 |
1͵2 |
7 |
Students will be able to use the method of separation of variables in order to solve some basic partial differential equations via Fourier series. |
1͵11 |
1͵2 |