Mathematical Analysis 1 (Engineering Sciences)

Fall 2025/26        Instructor: Prof. Jonathan Ben-Artzi

Timeline

The table below shows what we expect to cover each class during the semester. As the semester progresses I will be updating this table, so please refresh frequently. Clicking on the week number to the right will take you to that week's homework assignment.
Monday
Tuesday
Wednesday
Thursday

Homework

September

 

22 (notes)

1 BASIC NOTIONS

1.1 Sets

23 (notes)

1.1 Sets

1.2 Elements of mathematical logic

24 (notes)

1.2 Elements of mathematical logic

1.3 Sets of numbers

25 (notes)

1.3 Sets of numbers

1

29 (notes)

1.3 Sets of numbers, cardinality

1.4 Cartesian product

30 (notes)

1.5 Relations in the plane

1.6 Factorials and binomial coefficients

1 (notes)

2 FUNCTIONS

2.1 Functions: definitions and examples

2.2 Range and pre-image

2

CANCELLED

2

October

 

6 (notes)

2.3 Surjectivity, injectivity and invertibility

7 (notes)

2.4 Monotone functions

2.5 Composition of functions

2.6 Elementary functions and properties

8 (notes)

2.6 Elementary functions and properties

3 VECTORS AND COMPLEX NUMBERS

3.1 Polar, cylindrical and spherical coordinates

9 (notes)

3.2 Vectors in the plane and space

3.3 Complex numbers

3

13 (notes)

4 LIMITS AND CONTINUITY

4.1 Neighborhoods

4.2 Limits of sequences

14 (notes)

4.3 Limits of functions

15 (notes)

4.3 Limits of functions

16 (notes)

Exercises

4

20 (notes)

5 PROPERTIES AND COMPUTATION OF LIMITS

5.1 Uniqueness of the limit and local sign of a function

5.2 Algebra of limits

21 (notes)

5.3 Comparison theorems

5.4 Indeterminate forms and algebra type

22 (notes)

5.5 Substitution Theorem

5.6 Theorems on limits of sequences

23 (notes)

5.7 Fundamental limits and indeterminate forms of exponential type

5

27 (notes)

Exercises

28 (notes)

6 LOCAL COMPARISON OF FUNCTIONS

6.1 Landau symbols

29 (notes)

6.2 Infinitesimal and infinite functions

6.3 Order and principal part of infinitesimals and infinites

6.4 Asymptotes

30 (notes)

7 GLOBAL PROPERTIES OF CONTINUOUS MAPS

7.1 Theorem of Existence of Zeroes

6

November

 

3 (notes)

7.2 Range of a continuous map defined on an interval

7.3 Invertibility of continuous functions

4 (notes)

7.4 Lipschitz and uniformly continuous functions

5 (notes)

Exercises

6 (notes)

8 DIFFERENTIAL CALCULUS

8.1 The derivative

7

10 (notes)

8.2 Differentiation rules

8.3 Where differentiability fails

11 (notes)

8.4 Extrema and critical points

8.5 The Theorems of Rolle, Lagrange and Cauchy

12 (notes)

8.6 First and second finite increment formulas

8.7 Monotonicity intervals

13 (notes)

8.8 Higher-order derivatives

8

17 (notes)

8.9 Convexity and inflection points

18 (notes)

8.10 Qualitative study of a function

8.11 De l'Hôpital's Theorem

19 (notes)

Exercises

20 (notes)

9 TAYLOR EXPANSIONS AND APPLICATIONS

9.1 Taylor formulas

9

24 (notes)

9.2 Expanding the elementary functions

9.3 Operations on Taylor expansions

25 (notes)

9.4 Local behavior of a map via its Taylor expansion

26 (notes)

Exercises

27 (notes)

10 INTEGRAL CALCULUS

10.1 Primitive functions and indefinite integrals

10

December

 

1 (notes)

10.2 Rules of indefinite integration

2 (notes)

10.3 Definite integrals

3 (notes)

10.4 Cauchy integral

4 (notes)

10.5 Riemann integral

11

8

Holiday

9 (notes)

10.6 Properties of the definite integral

10.7 Integral mean value

10 (notes)

10.8 Fundamental Theorem of Integral Calculus

11 (notes)

10.9 Rules of definite integration

12

15 (notes)

Exercises

16 (notes)

11 IMPROPER INTEGRALS AND NUMERICAL SERIES

11.1 Improper integrals

17 (notes)

11.1 Improper integrals

18 (notes)

11.2 Numerical series

13

22 (notes)

11.2 Numerical series

23 (notes)

Exercises

24

Winter Break

25

Winter Break

29

Winter Break

30

Winter Break

31

Winter Break

1

Winter Break

January

 

5

Winter Break

6

Winter Break

7 (notes)

14 APPLICATIONS FROM THE REAL WORLD

8 (notes)

14 APPLICATIONS FROM THE REAL WORLD

14

12 (notes)

REVIEW AND RECAP

13 (notes)

REVIEW AND RECAP

14 (notes)

Exercises

15 (notes)

Exercises

15


Mock Exam:
 		TBA



EXAM DATES



Session
 		Written Exam (9:00-12:00)
 		Oral Exam



1
 		26 January 2026 (aula 2)
 XX January 2026
2
 		10 February 2026 (aule 6+7) XX February 2026



3
 		4 June 2026 (aula 2) XX June 2026
4
 		11 June 2026 (aula 2) XX June 2026



5
 8 September 2026 (aula 2) XX September 2026
6
 15 September 2026 (aula 2) XX September 2026