Analyse I (anglais)
MATH-101(en)
Media
29899
Week 14 Monday Lecture
07.01.2026, 15:09
Lecture of 15/12/2025 for Math-101(en) given by Leonid Monin.
MATH-101(en) Lecture 25 / Week 14
21.12.2025, 16:45
MATH-101(en) Lecture 24 / Week 13
17.12.2025, 15:32
MATH-101(en) Lecture 23 / Week 13
08.12.2025, 14:33
MATH-101(en) Lecture 22 / Week 12
05.12.2025, 00:54
MATH-101(en) Lecture 21 / Week 12
05.12.2025, 00:47
MATH-101(en) Lecture 20 / Week 11
26.11.2025, 18:25
MATH-101(en) Lecture 19 / Week 10
24.11.2025, 11:00
MATH-101(en) Lecture 18 / Week 10
18.11.2025, 16:21
MATH-101(en) Lecture 17 / Week 9
12.11.2025, 18:51
MATH-101(en) Lecture 16 / Week 9
12.11.2025, 18:47
MATH-101(en) Lecture 15 / Week 8
08.11.2025, 15:51
MATH-101(en) Lecture 14 / Week 8
03.11.2025, 12:37
MATH-101(en) Lecture 13 / Week 7
03.11.2025, 12:34
MATH-101(en) Lecture 12 / Week 7
03.11.2025, 12:32
MATH-101(en) Lecture 11 / Week 6
03.11.2025, 12:30
MATH-101(en) Lecture 10 / Week 6
03.11.2025, 12:28
MATH-101(en) Lecture 9 / Week 5
03.11.2025, 12:25
MATH-101(en) Lecture 8 / Week 5
07.10.2025, 13:19
MATH-101(en) Lecture 7 / Week 4
07.10.2025, 13:15
MATH-101(en) Lecture 6 / Week 4
07.10.2025, 13:11
MATH-101(en) Lecture 5 / Week 3
07.10.2025, 13:06
MATH-101(en) Lecture 4 / Week 2
19.09.2025, 13:23
MATH-101(en) Lecture 3 / Week 2
19.09.2025, 13:20
MATH-101(en) Lecture 2 / Week 1
15.09.2025, 09:25
Lecture of 10/09/2025 for Math-101(en) given by Leonid Monin.
MATH-101(en) Lecture 1 / Week 1
15.09.2025, 09:21
Lecture of 08/09/2025 for Math-101(en) given by Leonid Monin.
19, MATH-101(en) / Quiz for Chapters 8-9: Solutions
09.01.2022, 17:00
20.2, MATH-101(en) / Mock Exam 2020: Solutions to the TF questions
30.12.2021, 12:40
20.1, MATH-101(en) / Mock Exam 2020: Solutions to the QCM questions
30.12.2021, 12:38
18.1, MATH-101(en) / Quiz for Chapters 6-7: Solutions to the TF questions
30.12.2021, 12:23
18.2, MATH-101(en) / Quiz on Chapters 6-7: Solutions to the QCM questions
30.12.2021, 12:23
14.2, MATH-101(en) / Week 14: Power series and Taylor series
22.12.2021, 10:43
Lecture 27:
- Properties of improper integrals;
- Comparison theorem for improper integrals;
- Power series: definition;
- Domain of convergence, derivative, integrals;
- Taylor series.
14.1, MATH-101(en) / Week 14: Improper integrals
20.12.2021, 10:26
Lecture 26:
- More examples of integration by substitution;
- Integrating rational functions;
- Improper integrals: basic definitions.
17.2, MATH-101(en) / Quiz on Chpaters 4-5: Solutions to the TF questions
19.12.2021, 19:08
17.1, MATH-101(en) / Quiz on Chapters 4-5: Solutions to the QCM questions
19.12.2021, 19:07
15.2, MATH-101(en) / Quiz on Chapters 1-3: Solutions to TF questions
19.12.2021, 19:05
15.1, MATH-101(en) / Quiz on Chapters 1-3: Solutions to QCM questions
19.12.2021, 19:01
I re-uploaded the video, which I can see well on my PC, but it still displays the same issue.
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13.2, MATH-101(en) / Week 13: Integration by substitution
15.12.2021, 10:58
Lecture 25:
- Proofs and observations on the FTC;
- Integration by substitution;
- Examples.
13.1, MATH-101(en) / Week 13: Fundamental Theorem of Calculus
13.12.2021, 12:48
Lecture 24:
- Integrability and first properties;
- Anti-derivatives of a function;
- Fundamental Theorem of Calculus;
- Integration by parts.
12.2, MATH-101(en) / Week 12: Convexity and Concavity
08.12.2021, 11:10
Lecture 23:
- Inflection points and higher derivatives;
- Convexity and concavity;
- examples and applications;
- Asymptotes;
- Integration: motivation and Darboux sums.
12.1, MATH-101(en) / Week 12: Application of Taylor's approximation formula
06.12.2021, 17:53
Lecture 22:
- Taylor formula and composition of functions;
- How to compute limits with Taylor formula;
- Detecting local maxima and local minima using higher derivatis;
- Inflection points.
11.2, MATH-101(en) / Week 11: Taylor's approximation
01.12.2021, 16:26
Lecture 21:
- application of the Mean Value Theorem;
- l'Hopital rule;
- Taylor's approximation formula;
- Examples.
11.1, MATH-101(en) / Week 11: Rolle's and Mean Value Theorem
30.11.2021, 10:58
Lecture 20:
- Higher derivatives;
- Local extrema and stationary points;
- How to find the global max/min of a continuous function over a bounded interval;
- Rolle's Theorem;
- Mean Value Theorem.
10.2, MATH-101(en) / Week 10: Computing derivatives
24.11.2021, 10:21
Lecture 19:
- Derivatives and algebraic operations;
- the exponential function;
- Derivatives of compositions of functions;
- Derivatives of inverse function;
- Left and right derivatives.
16.3, MATH-101(en) / Mock Exam: Solutions to the open question
23.11.2021, 14:12
16.2, MATH-101(en) / Mock exam: Solutions to TF questions
23.11.2021, 14:11
16.1, MATH-101(en) / Mock exam: Solutions to QCM questions
23.11.2021, 14:11
10.1, MATH-101(en) / Week 10: Differentiability
22.11.2021, 15:14
Lecture 18:
- More on continuous strictly monotone functions and their inverses;
- Differentiability;
- Differentiability implies continuity;
- Examples.
9.2, MATH-101(en) / Week 9: Intermediate value theorem
17.11.2021, 13:09
Lecture 17:
- More on uniform continuity;
- Intermediate value theorem;
- monotonicity and continuity.
9.1, MATH-101(en) / Week 9: Continuous functions on a closed bounded interval
15.11.2021, 10:26
Lecture 15:
- Limits from the left and the right;
- Range of a continuous function on a closed bounded interval;
- Uniform continuity.
8.1, MATH-101(en) / Week 8: continuity
10.11.2021, 11:34
Lecture 14:
- Characterization of limits via sequences: examples.
- Squeeze theorem for limits.
- Limits and algebraic operations.
- Examples.
- Continuity and algebraic operations.
8.2, MATH-101(en) / Week 8: limits at infinity
10.11.2021, 11:11
Lecture 15:
- Composition of functions.
- Composition and continuity.
- Infinite limits.
- Limits at infinity.
7.2, MATH-101(en) / Week 7: Limits
03.11.2021, 10:49
Lecture 13:
- More about property of function;
- Pointed neighborhood;
- Limits of functions;
- Characterization of limits via sequences.
7.1, MATH-101(en) / Week 7: functions
01.11.2021, 22:15
Lecture 12:
- Cauchy's convergence criterion;
- D'Alembert's convergence criterion;
- Basic definitions about functions;
- Examples.
6.2, MATH-101(en) / Week 6: Criteria for the convergence of series
27.10.2021, 10:29
Lecture 11:
- Squeeze theorem for series;
- Examples;
- Leibniz criterion.
6.1, MATH-101(en) / Week 6: Cauchy sequences and introduction to series
25.10.2021, 10:44
Lecture 10:
- Cauchy sequences;
- liminf and limsup;
- series: definition and example;
- basic convergence criteria for series.
5.2, MATH-101(en) / Week 5: Subsequences and the Bolzano-Weierstrass theorem
20.10.2021, 11:05
Lecture 9:
- Squeeze theorem for unbounded sequences;
- Limits of monotone sequences;
- Subsequences: definitions and properties;
- Bolzano-Weierstrass theorem.
5.1, MATH-101(en) / Week 5: Limits of unbounded sequences
18.10.2021, 12:58
Lecture 8:
- Limits of recursive sequences;
- Limits of unbounded sequences;
- limits at infinity and algebraic operations.
4.2, MATH-101(en) / Week 4: Squeeze Theorem
13.10.2021, 15:25
Lecture 7:
- Squeeze Theorem;
- Quotient criterion;
- Recursive sequences and their limits.
4.1, MATH-101(en) / Week 4: Limits of sequences
11.10.2021, 13:06
Lecture 6 (click on the lecture name to be sent to the video for it), online lecture:
- More on induction and Bernoulli's inequality;
- Limits of sequences;
- Limits and Algebra;
- Examples and computations.
3.2, MATH-101(en) / Week 3: Sequences
06.10.2021, 11:02
Lecture 5 (click on the lecture name to be sent to the video for it):
- Solving equations over the complex numbers;
- Sequences: definitions and examples;
- Induction;
- Binomials and Bernoulli's inequality;
3.1, MATH-101(en) / Week 3: Complex numbers
04.10.2021, 13:27
Lecture 4 (click on the lecture name to be sent to the video for it):
- Triangular inequality over the reals;
- Extended real line;
- Complex numbers and operations among them;
- Absolute value of complex numbers and triangular inequality;
- Polar form of a complex number.
2.2, MATH-101(en) / Week 2: more results on inf/sup, density of Q in R
29.09.2021, 12:21
Lecture 3 (click on the lecture name to be sent to the video for it):
- More results on inf/sup;
- Subset of the natural numbers always have minima;
- Integral part of a real number;
- Density of the rational numbers in the real numbers.
2.1, MATH-101(en) / Week 2: max/min, inf/sup
27.09.2021, 13:24
Lecture 2:
- More notation on number sets and intervals;
- Upper and lower bounds: definitions, properties, examples;
- Maximum and minimum: definitions, properties, examples;
- Supremum and infimum: definitions, properties, examples.
(The video appears to have had some issues in terms of streaming. I will make sure that this gets fixed for the next lecture streamed from PO01)
1, MATH-101(en) / Week 1: Introduction to Analysis
22.09.2021, 13:18
Lecture 1:
- Motivations;
- Proofs;
- Sets;
- Number sets;
- Properties of the real numbers
MATH-101(en) / Week 14: Power series and Taylor series
16.12.2020, 13:39
MATH-101(en) / Week 14: Improper integrals
14.12.2020, 10:31
MATH-101(en) / Week 13: Integration: more examples and rational functions
09.12.2020, 10:59
MATH-101(en) / Week 13: Fundamental theorems of calculus and computing techniques
07.12.2020, 10:35
Mock exam: solutions to QCM 7-8
02.12.2020, 13:05
Mock exam: solutions to QCM 4-6
02.12.2020, 12:59
MATH-101(en) / Week 12: Integration
02.12.2020, 10:54
Mock exam: solutions to QCM 1-3
30.11.2020, 23:37
Mock exam: solutions to TF
30.11.2020, 12:03
MATH-101(en) / Week 12: Derivatives, local extrema, convexity/concavity
30.11.2020, 10:50
MATH-101(en) / Week 11: Taylor's approximation
25.11.2020, 10:58
MATH-101(en) / Week 11: L'Hôpital's rule
23.11.2020, 11:12
MATH-101(en) / Week 10: Rolle's Theorem and Mean Value Theorem
18.11.2020, 11:10
MATH-101(en) / Week 10: How to compute derivatives?
16.11.2020, 12:02
MATH-101(en) / Week 9: Differentiation
11.11.2020, 22:20
MATH-101(en) / Week 9: Intermediate Value Theorem
09.11.2020, 10:46
MATH-101(en) / Week 8: Limits and continuity, II
04.11.2020, 10:50
MATH-101(en) / Week 8: Limits at infinity
02.11.2020, 11:29
MATH-101(en) / Week 7: Limits & continuity
28.10.2020, 10:27
MATH-101(en) / Week 7: Limits
26.10.2020, 11:01
MATH-101(en) / Week 6: More convergence criteria for series & functions
21.10.2020, 12:35
MATH-101(en) / Week 6: Absolute convergence and Leibniz criterion
19.10.2020, 10:55
MATH-101(en) / Week 5: Cauchy sequences and Series
14.10.2020, 10:51
MATH-101(en) / Week 5: Subsequences and Bolzano-Weierstrass Theorem
12.10.2020, 10:40
MATH-101(en) / Week 4: Limits to infinity
07.10.2020, 10:56
MATH-101(en) / Week 4: Limits of sequences
05.10.2020, 10:58
MATH-101(en) / Week 3: Sequences
30.09.2020, 11:16
Math-101(en) / Week 3: Complex numbers.
28.09.2020, 13:16
MATH-101(en) / Week 2: Integral part, Absolute value, Density.
23.09.2020, 11:45
Math-101(en) / Week 2: Min/Max, Inf/Sup.
16.09.2020, 13:07
MATH-101(en) / Week 1: Introduction to Analysis
14.09.2020, 11:01
General Information
Course: MATH-101(en) Analysis 1 (English)
Teacher : Leonid Monin
Lectures
The lectures will be in the room CM 1105 on Mondays and Wednesdays.
The main lecture room has a capacity of 114 people. Due to the high number of enrolled students, lectures will also be streamed live via Zoom at: https://epfl.zoom.us/j/68714823417. Moreover, additional rooms have been reserved: CE15 on Mondays and CE1105 on Wednesdays.
First lecture: Monday September 8'th, 10h15-12h00, room.
Exercise Sessions
- Mondays, 8h15-10h00, rooms BS160 and BS170.
Evening Sessions
In addition to Exercise sessions there are extra evening sessions which work as office hours. The timetable for evening sessions is attached below.
Lecture recordings
The lecture recordings can be found here.
- Information about the course (URL)
- Exam information (Page)
- Exam seating arrangements (Folder)
- News forum (Forum)
- Book for the course: J. Douchet, B. Zwahlen, "Calcul différentiel et intégral", Presses polytechniques et universitaires romandes. (File)
- Approximate schedule and topics (Page)
- Full course (File)
- NOTES on Real functions (File)
- Timetable for evening sessions (File)
- Mock Exam (File)
- Solutions to Mock exam (File)
- Example open question (File)
- Solutions to Example open quesitons (File)
Week 1 (September 9 - September 14)
Lecture 1:
- Motivations;
- Proofs;
- Sets;
- Number sets;
- Properties of the real numbers.
Lecture 2:
- More notation on number sets and intervals ;
- Upper and lower bounds: definitions, properties, examples;
- Maximum and minimum: definitions, properties, examples;
- Supremum and infimum: definitions, properties, examples;.
- Axiom 2.22 and its consequences
Week 2 (September 16 - October 22)
Lecture 3:
- More results on inf/sup;
- Subset of the natural numbers always have minima;
- Integral part of a real number;
Lecture 4:
- Density of the rational numbers in the real numbers.
Week 3 (23 september- 29 september-
Lecture 5:
- Triangular inequality over the reals;
- Extended real line;
- Complex numbers and operations among them
Week 4 (30 September - October 6)
Lectures 6 and 7:
- Polar presentation of complex numbers
- Euler formula
- De Moivre's formula
- Solving equations over the complex numbers;
- Sequences: definitions and examples;
- Notes for Lecture 1-5 (File)
- Exercise sheet week 4 (File)
- Solutions Week 4 (File)
- Lecture 6 (File)
- Lecture 7 (File)
Week 5 (7 October - 13 October)
Lectures 8 and 9:
- Definition of limit and examples
- Algebra of Limits
- Squeeze Theorem
- Recursive sequences and their limits
- Infinite limits
Week 6 (October 14- October 18)
Lectures 10 and 11:
- Squeeze theorem.
- Quotient test
- limsup/liminf
- Subsequences: definitions and properties;
- Series
- Convergence and absolute convergence of series
Week 7 (October 28- November 3)
- Convergence and absolute convergence of Series
- Examples: Harmonic series, alternating harmonic series, geometric series
- Squeeze theorem for series
- Alternating series proposition
- Cauchy and d'Alemebert criterions
- Functions
Week 8 (November 4 - November 10)
Lectures 14 and 15
- Periodic functions
- Odd and even funcitons
- Limit of functions: two definitions
- Uniqueness of limit
- Infinite limits
- Continuous functions: definition
- Algebra of limits
Week 9 Nov 11-17
Week 10 (18 November - 24 November)
Continuous functions on intervals:
- Intermediate value theorem
- Injective continuous functions
- inverse functions
Derivatives:
- Definition and examples
- Derivative of sum, product, quotient of two functions
- Derivative of composition of two functions and of the inverse of a function
- Left and right derivatives
- Higher derivatives and C^k functions
Week 11 (25 November - 1 December)
Week 12 (2 December -8 December)
- Monotonicity and derivatives
- Taylor expansion
- Convex and concave functions
- Power series
- Taylor series
Week 13 (9 December - 15 December)
Week 14 (16 December - 22 December)
Week 14 (20 December - 24 December)
- More examples of integration by substitution;
- Integrating rational functions;
- Improper integrals: basic definitions.
- Properties of improper integrals;
- Comparison theorem for improper integrals;
- Power series: definition;
- Domain of convergence, derivative, integrals;
- Taylor series.
Previous Exams
- Final Exam 2018 (File)
- Final Exam 2019 (File)
- Final 2020 (File)
- 2019 soluti0ons and discussion (File)
- Answers for 2020 (File)
- Solutions for 2020 (File)
- Exam 2025 en (File)
- Exam 2025 en (solutions) (File)