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 |
MW is an extremely clear and well-written classic and definitely one of my favorites. Its biggest drawback is that it follows a "late transcendentals" concept, i.e., trigonometric functions, exponentials, and logarithms are introduced only after integration, which limits the variety of available examples at the time when the key ideas are first introduced. However, for self-study or review, this may not matter so much. This book is also freely and legally available as a scanned PDF download.
The book by Edwards and Penney is a good mainstream Calculus textbook. It used to be the default reading for many years at Jacobs, so there are still quite a few paper copies in the IRC.
RHB is a comprehensive textbook on mathematical methods that covers a great variety of concepts, far beyond first-year Calculus. The introductory chapters are somewhat terse and assume familiarity with high-school Calculus without presenting a systematic introduction from scratch. Yet, the choice of examples and focus on advanced topics make this book a lasting resource.
For the short Linear Algebra part at the end, the class mostly follows RHB except for the details of the process of Gaussian elimination and matrix inversion, which are covered by separate class notes. LADW is good background reading; the book is more advanced than what we are doing, but follows the same style and philosophy. Gaussian elimination is explained in the same way as here (except for a differen sign convention).
02/09/2020: | Introduction; natural numbers, integers, rational, real numbers (CLP1 0.1, additional reading CLP1 0.2, 0.3) |
07/09/2020: | Complex numbers
(RHB 3.1, 3.2); polynomials, factorization, fundamental theorem of Algebra (RHB 1.1) |
09/09/2020: | Long division
(see, e.g., CLP2, 1.10.1 or
the Wikipedia
article on Polynomial Long Division for a detailed explanation in North
American notation; I personally prefer the more self-explanatory
continental European tradition, see the
the Wikipedia
article on Long Division for a comparison of notation); intervals, inequalities (MW R2) |
14/09/2020: | Equations, graphs, functions (domain, range, inverse); brief review of elementary examples (trigonometric functions, exponential, logarithm) (CLP1 0.4-0.6, MW R4-R6) |
16/09/2020: | Limits of functions (CLP1 1.3, start with 1.4) |
21/09/2020: | Asymptotes (parts of CLP1 1.5); squeeze law and basic trigonometric limit (CLP1 1.4 ctd., also see CLP1 2.8 for the basic trigonometric limit) |
23/09/2020: | Continuity, types of discontinuities, intermediate value theorem
(CLP1 1.6); continuous functions attain their extreme values on closed, bounded intervals (CLP1 3.5.2) |
28/09/2020: | Differentiability, derivative, slope, secant, tangent (CLP1 2.1-2.3) |
30/09/2020: | Rules and theorems for differentiation, power
rule, product rule
(CLP1 2.4, 2.5 for advanded background reading, 2.6 for
examples); chain rule (CLP1 2.9) |
05/10/2020: | Derivatives of exp, log and trigonometric
functions
(parts of CLP1 2.7, 2.8, 2.10); implicit differentiation and derivative of inverse functions (CLP1 2.11, also MW 2.4); curvature of a function as an example (cf. RHB 2.1.9, but implicit differentiation makes this much easier) |
07/10/2020: | Rolle's theorem, mean value theorem, critical point, maximum/minimum of a function (parts of CLP1 2.13) |
12/10/2020: | First and second derivative tests, inflection points, isoperimetric problems (CLP1 2.13 ctd., 2.14, parts of 3.5) |
14/10/2020: | Curve sketching (CLP1 3.6) |
19/10/2020: | Anti-derivative, indefinite integral, integration by substitution, integration by parts (CLP1 4.1, CLP2 1.4, 1.7 - indefinite integral versions only) |
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 |