Instructor: | Marcel Oliver |
Email: | m.oliver@jacobs-university.de |
Phone: | 200-3212 |
Office hours: | Tu 11:00, We 10:00 in Research I, 107 |
TA: | Denida Blloshmi, d.blloshmi@jacobs-university.de |
Bishoy Kaleny, b.kaleny@jacobs-university.de |
Lectures: | Mo, We 14:15-15:30, on Teams |
02/09/2020: | Introduction; natural numbers, integers, rational, real numbers |
07/09/2020: | Complex numbers; polynomials, factorization, fundamental theorem of Algebra |
09/09/2020: | Long division; intervals, inequalities even/odd, composition |
14/09/2020: | Equations, graphs, functions (domain, range, inverse); brief review of elementary examples (trigonometric functions, exponential, logarithm) |
16/09/2020: | Limits of functions |
21/09/2020: | Continuity, types of discontinuities |
23/09/2020: | Upper and lower bound theorem, intermediate value theorem, affine functions |
28/09/2020: | Differentiability, derivative, slope, secant, tangent |
30/09/2020: | Rules and theorems for differentiation, power rule, product rule, chain rule |
05/10/2020: | Derivatives of exp, log and trigonometric functions, curvature of a function |
07/10/2020: | Rolle's theorem, mean value theorem, critical point, maximum/minimum of a function |
12/10/2020: | First and second derivative tests, inflection points, Isoperimetric problem, Newton's method |
14/10/2020: | Curve sketching |
19/10/2020: | Anti-derivative, indefinite integral, integrable, rules for integration |
21/10/2020: | Approximations to area, partitions of intervals, Riemann sum, definite integral, Fundamental theorem of Calculus |
26/10/2020: | Second fundamental theorem of Calculus, integration by substitution, integration by parts |
28/10/2020: | Review |
02/11/2020: | Mock Midterm Exam |
04/11/2020: | Applications of the integral I |
09/11/2020: | Applications of the integral II |
11/11/2020: | Basic analytic geometry: Lines and circles in cartesian plane, vectors/scalars, basis vectors for cartesian plane, components vs. coordinates, magnitude, scalar product, vector product, orthonormal basis, equations of lines/planes/spheres |
16/11/2020: | Vector spaces, span, linear dependence, dimension, basis vectors |
18/11/2020: | Matrix-vector multiplication, vector space of matrices, matrix multiplication, identity matrix, null matrix |
23/11/2020: | Systems of linear equations, Gaussian elimination |
25/11/2020: | Solutions of linear systems of equations, rank, nullspace, nullity, homogeneous, inhomogeneous |
30/11/2020: | Rank plus nullity theorem, examples, matrix inverse, regular/singular matrix |
02/12/2020: | Row operations of Gaussian elimination as linear opera- tors, matrix inverse with Gaussian elimination |
07/12/2020: | Review for final exam |
TBA: | Final Exam |