Engineering Mathematics 1

coursetab

c_weekno Title Body
1-1 Chap 7. Linear Algebra: Matrices, Vectors, Determinants. 7.1 Matrices, Vectors 7.2 Matrix Multiplication
1-2 7.3 Linear Systems of Equations. Gauss Elimination 7.4 Linear Independence. Rank of a Matrix. Vector Space 7.5 Solutions of Linear Systems
10-1 4.3 Constant-coefficient systems. Phase plane method 4.4 Criteria for critical points. Stability
10-2 4.5 Qualitative methods for nonlinear systems 4.6 Nonhomogeneous linear systems of ODEs
11-1 Chap 5. Series Solutions of ODEs 5.1 Power series method 5.2 Theory of the power series method
11-2 5.3 Legendre\'s equation 5.4 Frobenius method
12-1 5.5 Bessel\'s Equation 5.6 Bessel\'s functions of the second kind
12-2 5.7 Sturm-Liouville problems. Orthogonal functions 5.8 Orthogonal eigenfunction expansions
2-1 7.6 Second- and Third Order Determinants 7.7 Determinants. Cramer\'s Rule 7.8 Inverse of a Matrix. Gauss-Jordan Elimination
2-2 Chap 8. Linear Algebra: Matrix Eigenvalue Problems 8.1 Eigenvalues, Eigenvectors 8.2 Applications
3-1 8.3 Symmetic, Skew-Symmetric, and Orthogonal Matrices 8.4 Eigenbases. Diagonalization. Quadratic Forms
3-2 Chap 1. First Order ODEs 1.1 Basic concepts. 1.2 Geometric meaning of direction fields 1.3 Separable ODEs
4 No Class (Public Holiday)
5-1 1.4 Exact ODEs. Integrating factors 1.5 Linear ODEs. Bernoulli equation
5-2 No Class (National Holiday)
6-1 1.6 Orthogonal trajectories 1.7 Existence and uniqueness Chap 2. Second Order Linear ODEs 2.1 Homogeneous linear ODEs of second order
6-2 2.2 Homogeneous linear ODEs with constant coefficients 2.3 Differential operator 2.4 Modeling: Free Oscillations
7-1 2.5 Euler-Cauchy equation 2.6 Existence and uniqueness: Wronskian
7-2 2.7 Nonhomogeneous ODEs 2.8 Modeling: Forced Oscillations 2.9 Modeling: Electric circuits 2.10 Solution by variation of parameters
8-1 No Class
8-2 Midterm exam.
9-1 Chap 3. Higher-Order Linear ODEs 3.1 Homogeneous linear ODEs 3.2 Homogeneous linear ODEs with constant coefficients 3.3 Nonhomogeneous linear ODEs
9-2 Chap 4. Systems of ODEs 4.1 Systems of ODEs as models 4.2 Basic theory of systems of ODEs