Paul Zegeling
    Department Wiskunde
    Universiteit Utrecht
    tel: 030-2533720

Basic Mathematics: Calculus
Fall semester of 2015/2016

Course code: UCSCIMAT11


Boek: D.W. Jordan & P. Smith (JS); Mathematical Techniques, Oxford University Press.

Syllabus (with extra exercises): see [here]

Week 36

DAY 1: Tuesday 31-8-'15, 9:00-10:45
Lecture on: Review of differentiation and integration
Reading: 1.1–1.12, (1.17-1.18), 2.1–2.5, 2.7–2.10, 3.1-3.4, (3.5-3.6), (3.10), 4.1-4.5, 14.1-14.3, 15.1, 15.3-15.4, (15.8-15.9), 15.10

DAY 2: Thursday 3-9-'15, 13:45-15:30
Exercises: 15.2adg, 15.3ehm, ST4.4, 4.10b, 15.10 (=> Felix Nolet)
Week 37

DAY 3: Tuesday 8-9-'15, 9:00-10:45
Lecture on: Introduction to differential equations (=> Barbara van den Berg)
Reading: 18.1-18.2, 22.1, 23.5

DAY 4: Thursday 10-9-'15, 13:45-15:30
Exercises: 18.2chi, 18.3abef, 18.5*, 18.6*, 22.1abcdgh, ST23.3, 22.11a*
Week 38

DAY 5: Tuesday 15-9-'15, 9:00-10:45
Lecture on: Separation of variables, partial fractions (=> Barbara van den Berg)
Reading: 22.3, 1.14, 17.6

DAY 6: Thursday 17-9-'15, 13:45-15:30
Exercises: 22.4, 22.5*, 1.36ac, 17.8abdg, 22.9*, 23.2bd
Week 39

DAY 7: Tuesday 22-9-'15, 9:00-10:45
Lecture on: Substitution, integration by parts
Reading: 17.1-17.5, 17.7-17.8, 22.5

DAY 8: Thursday 24-9-'15, 13:45-15:30
Exercises: 17.2abcd, 17.3efjk, 17.4ck, 17.5ajm, 17.7ab, 17.8i, 17.10cei, 17.13cej, 17.17*, 22.18*, 22.12be
Week 40

DAY 9: Tuesday 29-9-'15, 9:00-10:45
Lecture on: Second-order differential equations
Reading: 18.3, 18.5, 19.1, 19.3-19.4

DAY 10: Thursday 1-10-'15, 13:45-15:30
Exercises: 18.7bfin, 18.9abef, 19.1bcfh, 19.3ac, 19.5cf, 19.9*
Week 41

DAY 11: Tuesday 6-10-'15, 9:00-10:45
Lecture on: Complex numbers and differential equations
Reading: 6.1-6.5, (6.7), 18.4, 19.2

DAY 12: Thursday 8-10-'15, 13:45-15:30
Exercises: 6.1, 6.2, 6.7, 6.10abc, 6.11fgi, 6.12*, 6.16c, 6.19, 6.20bd, 18.10dj, 18.11ac, 18.15*, 19.2aeg, 19.5agj
Week 42

DAY 13: Tuesday 13-10-'15, 9:00-10:45
Preparations for the midterm exam!

DAY 14: Thursday 15-10-'15, 13:45-15:30
MID TERM EXAM
Week 43 (October 17-25): NO LECTURES! (Fall break)
Week 44

DAY 15: Tuesday 27-10-'15, 9:00-10:45
Lecture on: Phase plane analysis
Reading: (23.1-23.3), 23.5-23.6

DAY 16: Thursday 29-10-'15, 13:45-15:30
Exercises: Exercises: 23.2, 23.5, 23.10*
Week 45

DAY 17: Tuesday 3-11-'15, 9:00-10:45
Lecture on: Taylor expansions
Reading: (1.15-1.16), 5.1-5.5, 5.7

DAY 18: Thursday 5-11-'15, 13:45-15:30
Exercises: Exercises: 5.1acg, 5.2ce, 5.4ce, 5.5abf, 5.6ab, 5.10ab, 5.11a*
Week 46

DAY 19: Tuesday 10-11-'15, 9:00-10:45
Lecture on: Vectors, scalar product
Reading: (9.1-9.3), 9.4, 9.7, 10.1-10.3

DAY 20: Thursday 12-11-'15, 13:45-15:30
Exercises: 9.7, 9.8, 9.9, 9.12*, 9.28, 9.29, 10.5, 10.6, 10.8, 10.13, 10.15
Week 47

DAY 21: Tuesday 17-11-'15, 9:00-10:45
Lecture on: Matrices
Reading: (10.4), (10.6), 7.1-7.4, 8.1-8.2, 13.3

DAY 22: Thursday 19-11-'15, 13:45-15:30
Exercises: 7.3, 7.6, 7.8*, 7.11, 7.12, 7.14abc, 7.15, 8.1cf, 8.2, 8.4bc, 8.8, 13.11
Week 48

DAY 23: Tuesday 24-11-'15, 9:00-10:45
Lecture on: Diagonalisation
Reading: (12.4-12.5), 13.1-13.2, 13.4-13.5, (23.7)

DAY 24: Thursday 26-11-'15, 13:45-15:30
Exercises: 12.4, 12.8, 12.16, 13.1ab, 13.4ac, 13.8, 13.12, 13.13, 13.14, 13.17
Week 49

DAY 25: Tuesday 1-12-'15, 9:00-10:45
Lecture on: Functions of several variables and unconstrained optimisation
Reading: 28.1-28.4, 28.5, (31.1, 31.4, 31.7)

DAY 26: Thursday 3-12-'15, 13:45-15:30
Exercises: 28.1cef, 28.2bc, 28.3aefimp, 28.8c, 28.10abcf, 28.12acdfhn, 28.15
Week 50

DAY 27: Tuesday 8-12-'15, 9:00-10:45
Lecture on: Geometry of multivariate functions and constrained optimisation
Reading: 29.1-29.3, 29.6, 29.5, 31.5, (9.6), (10.8-10.9), 30.1-30.2, (31.3), (31.8)

DAY 28: Thursday 10-12-'15, 13:45-15:30
Exercises: 29.9a, 29.9abdf, 29.21abe, 29.19a, 29.23abcd, 31.12abeg, 30.1abcg, 30.5, 30.2abcd, 31.21de, 9.25*
Week 51

DAY 29: Tuesday 15-12-'15, 9:00-10:45
Exercises and rehearsal for final exam

DAY 30: Thursday 17-12-'15, 13:45-15:30
FINAL EXAM