Mathematical Analysis 1 Fall 2026/27

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	21 (notes) 1 BASIC NOTIONS 1.1 Sets	22 (notes) 1.1 Sets 1.2 Elements of mathematical logic	23 (notes) 1.2 Elements of mathematical logic 1.3 Sets of numbers	24 (notes) 1.3 Sets of numbers	1 Solutions
September	28 (notes) 1.3 Sets of numbers, cardinality 1.4 Cartesian product	29 (notes) 1.5 Relations in the plane 1.6 Factorials and binomial coefficients	30 (notes) 2 FUNCTIONS 2.1 Functions: definitions and examples 2.2 Range and pre-image	1 (notes) 2.3 Surjectivity, injectivity and invertibility	2 Solutions
October	5 (notes) 2.4 Monotone functions 2.5 Composition of functions	6 (notes) 2.5 Composition of functions 2.6 Elementary functions and properties	7 (notes) 2.6 Elementary functions and properties	8 (notes) 3 COMPLEX NUMBERS 3.3 Complex numbers	3 Solutions
	12 (notes) 3.3 Complex numbers 4 LIMITS AND CONTINUITY 4.1 Neighborhoods 4.2 Limits of sequences	13 (notes) 4.2 Limits of sequences	14 (notes) 4.2 Limits of sequences 4.3 Limits of functions	15 (notes) 4.3 Limits of functions	4 Solutions
	19 (notes) 4.3 Limits of functions	20 (notes) 4.3 Limits of functions 5 PROPERTIES AND COMPUTATION OF LIMITS 5.1 Uniqueness of the limit and local sign of a function	21 (notes) 5.2 Algebra of limits 5.3 Comparison theorems	22 (notes) 5.4 Indeterminate forms of algebraic type 5.5 Substitution Theorem	5 Solutions
	26 (notes) 5.6 Theorems on limits of sequences 5.7 Fundamental limits and indeterminate forms of exponential type	27 (notes) 6 LOCAL COMPARISON OF FUNCTIONS 6.1 Landau symbols	28 (notes) 6.2 Infinitesimal and infinite functions 6.3 Order and principal part of infinitesimals and infinites	29 (notes) 6.4 Asymptotes 7 GLOBAL PROPERTIES OF CONTINUOUS MAPS 7.1 Theorem of Existence of Zeroes	6 Solutions
November	2 (notes) 7.2 Range of a continuous map defined on an interval	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) 8 DIFFERENTIAL CALCULUS 8.1 The derivative	7 Solutions
	9 (notes) 8.1 The derivative 8.2 Differentiation rules	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	8 Solutions
	16 (notes) 8.7 Monotonicity intervals 8.8 Higher-order derivatives	17 (notes) 8.9 Convexity and inflection points 8.10 Qualitative study of a function	18 (notes) 8.10 Qualitative study of a function 8.11 De l'Hôpital's Theorem	19 (notes) 9 TAYLOR EXPANSIONS AND APPLICATIONS 9.1 Taylor formulas	9 Solutions
	23 (notes) 9.2 Expanding the elementary functions	24 (notes) 9.3 Operations on Taylor expansions	25 (notes) 9.3 Operations on Taylor expansions	26 (notes) 9.4 Local behavior of a map via its Taylor expansion 10 INTEGRAL CALCULUS 10.1 Primitive functions and indefinite integrals	10 Solutions
December	30 (notes) 10.1 Primitive functions and indefinite integrals	1 (notes) 10.2 Rules of indefinite integration	2 (notes) 10.2 Rules of indefinite integration 10.3 Definite integrals	3 (notes) 10.4 Cauchy integral	11 Solutions
	7 (notes) 10.5 Riemann integral 10.6 Properties of the definite integral	8 Holiday	9 (notes) 10.6 Properties of the definite integral 10.7 Integral mean value 10.8 Fundamental Theorem of Integral Calculus	10 (notes) 10.8 Fundamental Theorem of Integral Calculus 10.9 Rules of definite integration	12 Solutions
	14 (notes) 10.9 Rules of definite integration 10.10 Diff. of integrals with functional limits 11 IMPROPER INTEGRALS AND NUMERICAL SERIES 11.1 Improper integrals	15 (notes) 11.1 Improper integrals	16 (notes) 11.1 Improper integrals 11.2 Numerical series	17 (notes) 11.2 Numerical series	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) 13 ORDINARY DIFFERENTIAL EQUATIONS 13.1 General definitions 13.2 First-order differential equations	14 Solutions
January	11 (notes) 13.3 The IVP for first-order equations	12 (notes) 13.4 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

Mathematical Analysis 1 (Engineering Sciences)

Fall 2026/27 Instructor: Prof. Jonathan Ben-Artzi

Timeline