Mathematical Analysis 1 (Engineering Sciences)

Fall 2026/27        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

Exercises

September

 

21 (notes)

BASIC NOTIONS

Sets

22 (notes)

Sets

Elements of mathematical logic

23 (notes)

Elements of mathematical logic

Sets of numbers

24 (notes)

Sets of numbers

1

Solutions

28 (notes)

Sets of numbers, cardinality

29 (notes)

Cartesian product

Relations in the plane

Factorials and binomial coefficients

30 (notes)

SEQUENCES
Sequences and subsequences

FUNCTIONS

Functions: definitions and examples

1 (notes)

Range and pre-image

Surjectivity, injectivity and invertibility

2

Solutions

October

 

5 (notes)

Monotone functions

Composition of functions

6 (notes)

Composition of functions

Elementary functions and properties

7 (notes)

Elementary functions and properties

8 (notes)

LIMITS AND CONTINUITY

Neighborhoods

Limits of sequences

3

Solutions

12 (notes)

Limits of sequences

13 (notes)

Limits of functions

14 (notes)

Limits of functions

15 (notes)

Limits of functions

4

Solutions

19 (notes)

PROPERTIES AND COMPUTATION OF LIMITS

Uniqueness of the limit and local sign of a function

20 (notes)

Algebra of limits

Comparison theorems

21 (notes)

Indeterminate forms of algebraic type

Substitution Theorem

22 (notes)

Theorems on limits of sequences

Fundamental limits and indeterminate forms of exponential type

5

Solutions

26 (notes)

Theorems on limits of sequences

Fundamental limits and indeterminate forms of exponential type

27 (notes)

SERIES

Landau symbols

LOCAL COMPARISON OF FUNCTIONS

Landau symbols

28 (notes)

Infinitesimal and infinite functions

Order and principal part of infinitesimals and infinites

29 (notes)

Asymptotes

GLOBAL PROPERTIES OF CONTINUOUS MAPS

Theorem of Existence of Zeroes

6

Solutions

November

 

2 (notes)

Range of a continuous map defined on an interval

3 (notes)

Range of a continuous map defined on an interval

Invertibility of continuous functions

4 (notes)

Lipschitz and uniformly continuous functions

5 (notes)

DIFFERENTIAL CALCULUS

The derivative

7

Solutions

9 (notes)

The derivative

Differentiation rules

10 (notes)

Differentiation rules

Where differentiability fails

11 (notes)

Extrema and critical points

The Theorems of Rolle, Lagrange and Cauchy

12 (notes)

First and second finite increment formulas

Monotonicity intervals

8

Solutions

16 (notes)

Monotonicity intervals

Higher-order derivatives

17 (notes)

Convexity and inflection points

Qualitative study of a function

18 (notes)

Qualitative study of a function

De l'Hôpital's Theorem

19 (notes)

TAYLOR EXPANSIONS AND APPLICATIONS

Taylor formulas

9

Solutions

23 (notes)

Expanding the elementary functions

24 (notes)

Operations on Taylor expansions

25 (notes)

Operations on Taylor expansions

26 (notes)

Local behavior of a map via its Taylor expansion

INTEGRAL CALCULUS

Primitive functions and indefinite integrals

10

Solutions

December

 

30 (notes)

Primitive functions and indefinite integrals

1 (notes)

Rules of indefinite integration

2 (notes)

Rules of indefinite integration

Definite integrals

3 (notes)

Cauchy integral

11

Solutions

7 (notes)

Riemann integral

Properties of the definite integral

8

Holiday

9 (notes)

Properties of the definite integral

Integral mean value

Fundamental Theorem of Integral Calculus

10 (notes)

Fundamental Theorem of Integral Calculus

Rules of definite integration

12

Solutions

14 (notes)

Rules of definite integration

Diff. of integrals with functional limits
IMPROPER INTEGRALS AND NUMERICAL SERIES

Improper integrals

15 (notes)

Improper integrals

16 (notes)

Improper integrals

Numerical series

17 (notes)

COMPLEX NUMBERS

Complex numbers

13

Solutions

21

CANCELLED

22

CANCELLED

23

Winter Break

24

Winter Break

28

Winter Break

29

Winter Break

30

Winter Break

31

Winter Break

January

 

4

Winter Break

5

Winter Break

6

Winter Break

7 (notes)

ORDINARY DIFFERENTIAL EQUATIONS

General definitions

First-order differential equations

14

Solutions

11 (notes)

The IVP for first-order equations

12 (notes)

Second-order equations

13 (notes)

SOLVE MOCK EXAM

14 (notes)

Last class:

REVIEW


EXAM DATES



Call
 		Written Exam (at the engineering faculty)
 		Oral Exam (at the math department)



1
 		XX January 2027
 XX January 2027
2
 		XX February 2027 XX February 2027



3
 		XX June 2027 XX June 2027
4
 		XX July 2027 XX July 2027



5
 XX September 2027
 XX September 2027
6
 XX September 2027
 XX September 2027