I will try to follow the following schedule, but I cannot rule out changes caused by higher causes (illness, natural disasters etc.) or by a flash of inspiration getting grip of me in the middle of a lecture.
Week 1:
a) Introduction. Errors in calculations. Representation of numbers.
Taylor expansion, big-O notation.
b) Numerical derivation. Numerical integration.
Printable slides:
Errors,
O-notation,
and
Integral and derivative.
Labs: Familiarization with Maple. Playing with errors and big-O.
Maple worksheet
Week 2:
a) Introduction to ODE. Method of separation. Theory: Peano's and Picard's theorem.
b) Slope field, stability of equilibria. Some popular applications.
Printable slides:
separable ODEs.
Labs: Separable ODEs. Slope fields.
Week 3:
a) Outline of method of variation.
Numerical solition of ODE: Discretization. Euler method.
Error estimate, order of method. Intro to FDM.
b) Second order methods. Runge-Kutta methods for ODE.
Estimating error via control method. RKF45.
Printable slides:
ODE - numerical view.
Labs: Separable ODEs.
Week 4:
a) Taylor method. Interpolation.
b) Homogeneous linear ODE. Theorems on solutions, characteristic numbers.
Printable slides:
interpolation,
linear ODE.
Labs: ODE in Maple.
Maple worksheet
Week 5:
a) Structural theorems. Linear ODE with a special RHS
(method of undetermined coefficients). Method of variation of constant.
b) Roots of functions: bisection, slices, Newton and others.
Printable slides:
Roots.
Labs: Homogeneous ODE's.
Week 6:
a) Fixed points, iteration, relaxation.
b) More on roots. Numerical methods for higher order LODE: Taylor method, FDM.
Printable slides:
Matrices.
Labs: Method of undetermined coefficients.
Week 7:
a) Systems of linear equations: GJM, GEM. LU(P) decomposition. Residual.
b) Norm of a matrix, condition number. Errors, stability.
Labs: Maple: Zeros of functions.
Maple worksheet
Week 8:
a) Fixed points and iterations for systems of lienar equations: JIM, GSM.
b) Homogeneous systems of linear ODEs. Eigenvalues and eigenvectors.
Printable slides:
systems of linear ODE.
Labs: Maple: Systems of linear equations.
Maple worksheet
Week 9:
a) Non-homogeneous systems of equations. Numerical methods for systems.
b) Examples of applications: Population dynamics, pendulum and spring, RLC circuits.
Labs:Midterm.
Solving homogeneous systems of ODE.
Week 10:
a) Eigenvalues and eigenvectors. Power iteration.
b) Review: Power series.
Printable slides:
Power series, transforms.
Labs: Solving systems of ODE. Variation.
Week 11:
a) Solving ODE using series. Transforms. Series as transform.
b) Fourier transform.
Printable slides:
Fourier transform.
Labs: Maple: Eigenvalues and eigenvectors.
Maple worksheet
Week 12:
a) Laplace transform.
b) Laplace transform of a finite signal, LT and systems.
Printable slides:
Laplace transform.
Labs: Laplace transform
Week 13:
a) Semestral project.
b) PDE's (intro). Review
Printable slides:
PDE,
Labs: Laplace transform.