Analyse I (anglais)

MATH-101(en)

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Click here to reach the channel of the course, where you can access the recordings of all lectures.
Links for each single lecture will be posted below in the corresponding week.

MATH-101(en) Analysis I (English) - Fall 2021

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.

Please click here to find the video to download/view online. 

You need to be logged in with your EPFL account to see it.

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) Analysis I (English) - Fall 2021

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.

Please click here to find the video to download/view online. 

You need to be logged in with your EPFL account to see it.

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