Mo 08:15 - 10:00 in ETA F 5
We 08:15 - 10:00 in HG F 1 with Livestream in HG F 3
Th 08:15 - 10:00 in ETA F 5
Introduction to differential and integral calculus in one real variable: Basic concepts of mathematical thinking, numbers, sequences and series, continuous functions, differentiable functions, ordinary differential equations, Riemannian integration.
Recordings: The lectures are recorded. The videos will be made available at the end of the semester so that you can use them in order to prepare for the exam.
Old Lecture Notes: Lecture Notes by Peter Jossen (Fall Semester 2019)
Disclaimer: The lecture in 2019 contained considerably more material than our lecture, the order of the topics was different (compare the table of contents) and many results were given in more generality.
| Week | # | Date | Topics | Chapters |
|---|---|---|---|---|
| 1 | 1 | 19.09. | Introduction | 1.1. |
| 2 | 21.09. | Ordered fields | 2.1.1 | |
| 2 | 3 | 25.09. | Properties of ordered fields, Absolute value, Sign | 2.1.1 |
| 4 | 27.09. | Axiom of completeness, Real numbers, Square Root, Intervals | 2.1.2 & 2.1.3 | |
| 5 | 28.09. | Neighbourhoods, Open and closed sets in \( \mathbb{R}\), Field of complex numbers, Complex conjugation | 2.1.3 & 2.2.1 | |
| 3 | 6 | 02.10. | Open and closed sets in \(\mathbb{C}\), Bounded Sets in \(\mathbb{R}\), Maxima and Minima, Suprema and Infima, Undefinite Values | 2.2.2 & 2.3.1 |
| 7 | 04.10. | Archimidean principle, Uncountability of \(\mathbb{R}\), Sequences and Convergence | 2.4.1, 2.4.2 & 2.5.1 | |
| 8 | 05.10. | Subsequences, Accumulation points | 2.5.1, 2.5.2 & 2.5.3 | |
| 4 | 9 | 09.10. | Sequences and Inequalities, Bounded sequences, Monotone sequences, Superior and Inferior limits | 2.5.3 & 2.5.4 |
| 10 | 11.10. | Superior and Inferior limit vs. Accumulation points, Bounded sequences and convergent subsequences, Cauchy Sequences | 2.5.4 & 2.5.5 | |
| 11 | 12.10. | Improper limits, Sequences of complex numbers, Bounded and Monotone Functions, Continuous Functions | 2.5.6, 2.5.7, 3.1.1 & 3.1.2 | |
| 5 | 12 | 16.10. | Combinations and Compositions of Continuous Functions, Sequential Continuity | 3.1.2 & 3.1.3 |
| 13 | 18.10. | Intermediate Value Theorem, Inverse Function Theorem | 3.2.1 & 3.2.2 | |
| 14 | 19.10. | Compact Intervals, Extreme Values, Uniform Continuity | 3.3.1 & 3.3.2 | |
| 6 | 15 | 23.10. | Exponential and Logarithm, Limits of Functions | 3.4.1, 3.4.2, 3.4.3 & 3.5.1 |
| 16 | 25.10. | Improper limits, One-sided limits, Limits at Infinity, Jumps, Landau Notation | 3.5.1, 3.5.2 & 3.5.3 | |
| 17 | 26.10. | Sequences of Functions, Pointwise convergence, Uniform convergence, Series of real numbers and convergence | 3.6.1, 3.6.2 & 4.1.1 | |
| 7 | 18 | 30.10. | Conditional convergence, Rearrangement Theorem, Leibniz and Cauchy criterion, Absolute convergence, Root and quotient criteria | 4.1.2, 4.1.3 & 4.2.1 |
| 19 | 01.11. | Reordering series, Products of series, Series of complex numbers, Power series, Radius of convergence | 4.2.2, 4.2.3, 4.3, 4.4.1 & 4.4.2 | |
| 20 | 02.11. | Exponential map as power series, Trigonometric functions, Circle number, Polar coordinates, Complex logarithm, Hyperbolic functions | 4.5.1, 4.5.2, 4.5.3, 4.5.4, 4.5.5 & 4.5.6 | |
| 8 | 06.11 & 08.11. | Repetition | ||
| 21 | 09.11. | Derivative, Higher Derivatives, Class \(C^n\), Smooth functions, Differentiation rules | 5.1.1 & 5.1.2 | |
| 9 | 22 | 13.11. | Derivative of the inverse, Local Extrema and the first Derivative, Rolle's Theorem and (Cauchy) Mean Value Theorem, L'Hopital's rule | 5.1.2, 5.2.1, 5.2.2 & 5.2.3 |
| 23 | 15.11. | L'Hopital's rule, Monotonicity and Convexity via Calculus, Differentiation of trigonometric functions | 5.2.3, 5.2.4 & 5.3.1 | |
| 24 | 16.11. | Differentiation of Trigonometric functions, Decompositions and Step functions, Integral of step functions, Riemann integrability | 5.3.1, 5.3.2, 5.3.3, 6.1.1, 6.1.2 & 6.2.1 | |
| 10 | 25 | 20.11. | Linearity and Monotonicity of integral, Triangle Inequality for integral, Integrability of monotone/continuous functions | 6.2.1, 6.2.2, 6.3.1 & 6.3.2 |
| 26 | 22.11. | Integration and sequences of functions, Primitve functions, Fundamental theorem of calculus | 6.3.3 & 7.1.1 | |
| 27 | 23.11. | Integration by parts and integration by substitution, Improper integrals, Integral test for series | 7.1.2 & 7.1.3 | |
| 11 | 28 | 27.11. | Integration and differentiation of power series, Integration methods | 7.2, 7.3.1, 7.3.2, & 7.3.3 |
| 29 | 29.11. | Integration methods, Improper integration limits | 7.3.3, 7.3.4, 7.3.5 & 7.3.6 | |
| 30 | 30.11. | Gamma function, Taylor approximation with big-O and little-o | 7.3.6 & 7.4.1 | |
| Points | Bonus |
|---|---|
| 1 | 0.1 |
| 2 | 0.2 |
| 3 | 0.25 |
Schedule: Exercise Sheet n will be posted on Monday of the (n+1)th week of the semester and is due by Wednesday of the (n+2)th week at 12:00. For instance, Exercise Sheet 2 will be posted on Monday of the 3rd week and will be due on Wednesay of the 4th week at 12:00.
Hand in: To hand in your solutions, please use the provided upload link (How to). Your uploads can be accessed exclusively by the tutor of your exercise group, so it is crucial that you choose a group on myStudies. In order to upload your solutions, you must be connected to an ETH-WiFi or use a VPN (How to).
| Exercise Sheet | Übungsserie | Due by | Upload link | Solutions |
|---|---|---|---|---|
| Exercise Sheet 0 | Übungsserie 0 | Wednesday 27.09. 12:00 | Submission | Lösungsblatt 0 |
| Exercise Sheet 1 | Übungsserie 1 | Wednesday 04.10. 12:00 | Submission | Lösungsblatt 1 |
| Exercise Sheet 2 | Übungsserie 2 | Wednesday 11.10. 12:00 | Submission | Lösungsblatt 2 |
| Exercise Sheet 3 | Übungsserie 3 | Wednesday 18.10. 12:00 | Submission | Lösungsblatt 3 |
| Exercise Sheet 4 | Übungsserie 4 | Wednesday 25.10. 12:00 | Submission | Lösungsblatt 4 |
| Exercise Sheet 5 | Übungsserie 5 | Wednesday 01.11. 12:00 | Submission | Lösungsblatt 5 |
| Exercise Sheet 6 | Übungsserie 6 | Wednesday 08.11. 12:00 | Submission | Lösungsblatt 6 |
| Exercise Sheet 7 | Übungsserie 7 | Wednesday 15.11. 12:00 | Submission | Lösungsblatt 7 |
| Exercise Sheet 8 | Übungsserie 8 | Wednesday 22.11. 12:00 | Submission | Lösungsblatt 8 |
| Exercise Sheet 9 | Übungsserie 9 | Wednesday 29.11. 12:00 | Submission | Lösungsblatt 9 |
| Exercise Sheet 10 | Übungsserie 10 | Wednesday 06.12. 12:00 | Submission | Coming on Wednesday 06.12. |
We 12:15 - 13:00 in HG E 33.3
Fr 08:15 - 10:00 in CAB G 52
We 13:15 - 14:00 in meetngroom 440 019 6465 on Zoom
Fr 08:15 - 10:00 in meetingroom 440 019 6465 on Zoom
We 12:15 - 13:00 in HG E 33.5
Fr 08:15 - 10:00 in CHN D 46
We 13:15 - 14:00 in HG E 33.5
Fr 08:15 - 10:00 in ETZ H 91
We 12:15 - 13:00 in HG F 26.5
Fr 08:15 - 10:00 in CLA E 4
We 13:15 - 14:00 in HG F 26.5
Fr 08:15 - 10:00 in HG G 26.3
We 12:15 - 13:00 in ML F 40
Fr 08:15 - 10:00 in LFW C 4
We 12:15 - 13:00 in ML H 41.1
Fr 08:15 - 10:00 in IFW A 34
We 13:15 - 14:00 in ML H 41.1
Fr 08:15 - 10:00 in CHN D 44
We 13:15 - 14:00 in ML F 40
Fr 08:15 - 10:00 in IFW C 33
We 12:15 - 13:00 in ML F 34
Fr 08:15 - 10:00 in LEE C 104
We 13:15 - 14:00 in ML F 34
Fr 08:15 - 10:00 in LEE C 114
We 12:15 - 13:00 in ML F 38
Fr 08:15 - 10:00 in LEE D 101
We 13:15 - 14:00 in ML F 38
Fr 08:15 - 10:00 in LEE D 105
We 12:15 - 13:00 in HG G 26.1
Fr 08:15 - 10:00 in LFW B 2
We 13:15 - 14:00 in LEE D 101
Fr 08:15 - 10:00 in CHN D 48
We 12:15 - 13:00 in LFW C 5
Fr 08:15 - 10:00 in NO C 44
We 13:15 - 14:00 in HG G 26.1
Fr 08:15 - 10:00 in ML J 34.3
We 13:15 - 14:00 in HG E 33.1
Fr 08:15 - 10:00 in HG G 26.1
We 12:15 - 13:00 in HG E 33.1
Fr 11:45 - 13:30 in HCI H 8.1
We 13:15 - 14:00 in CAB G 52
Fr 11:45 - 13:30 in HIT J 53