# Recommended exercises

Here is a plan for lectures, tutorials and seminars 2015-2016 with recommended exercises from  Calculus (8:e upplagan) by Adams och Essex (F means lecture, Ö means tutorial and Sem means seminar).

Module 1: Limits and continuity

F1       Ch P. Intro, numbers, functions, polynomials och trigonometry.

F2       Ch 1.1-1.3 + 1.5. Limits

Ö1       Exercises: P1: 7, 11, 19, 29, 39. P2: 13,15,17,23. P3: 3, 7, 43, 49.  P4: 1, 3, 7, 11, 31, 33, 53. P5: 9, 25. P6: 1, 7, 17. P7: 1, 3, 7, 19, 25, 26, 51.  1.2: 9, 13, 21, 25, 30, 49, 50, 78, 79. 1.3: 3, 6, 11, 13, 53. 1.5: 13, 29.

F3       Ch 1.4. Continuity.

Ö2       Exercises: 1.4: 7, 8, 12, 15, 17, 20, 21, 29.

Sem1 CH P and Ch 1. Hand-in.

Module 2: Differentiation

F4       CH 2.1-2.5. Definition of the derivative, differentiation rules

F5       Ch 2.6-2.8. Mean value theorem etc

Ö3       Exercises: 2.1: 5, 7. 2.2: 1, 3, 11, 26, 27, 40, 41, 42, 43, 44, 45, 47. 2.3: 1, 7,   11, 17, 25, 33, 35, 47. 2.4: 3, 5, 11, 18, 23, 30, 31, 37. 2.5: 13, 15, 23, 29, 31, 35, 45, 62. 2.6: 3, 9. 2.7: 1, 3, 11, 13, 23, 29. 2.8: 5, 13, 21, 27.

F6       Ch 2.9-2.11. Implicit differentiation etc

Ö4       Exercises: 2.9: 3, 9, 13. 2.11: 5, 7, 13, 16, 17, 18, 19.

Sem2 Ch 2. Written test

Module 3: Transcendental functions and ODE

F7       Ch 3.1-3.6. Transcendental functions.

F8       Ch 3.7. ODE intro. Homogeneous

Ö5       Exercises: 3.1: 3, 9, 23. 3.2: 3, 5, 9, 15, 25, 29. 3.3: 3, 5, 7, 9, 19, 21, 31, 33, 43, 51, 59. 3.4: 1, 3, 5, 9, 11, 17, 23, 25. 3.5: 1, 3, 5, 7, 13, 19, 21, 23, 35.  3.7: 1, 3, 5, 7, 9, 13, 15, 21, 25, 29.

F9       Ch 18.6. ODE cont. Inhomogeneous.

Ö6       Exercises: 18.6: 1, 3, 5, 7

Sem3  Ch 3. Hand-in.

Module 4: Applications of the derivative

F10     Ch 4.1-4.5. Applications. Max / min etc

F11     Ch 4.6-4.8. Appl. cont. Curve sketching etc

Ö7       Exercises: 4.1: 5, 7, 9, 16, 17. 4.2: 7, 9. 4.3: 1, 5, 17. 4.4: 3, 14, 29, 35.  4.5: 5, 11, 27, 31. 4.6: 3, 5, 9, 17, 31, 35. 4.8: 1, 7, 13, 21, 25, 31.

F12     Ch 4.9-4.10. Taylor's formula.

Ö8       Exercises: 4.9: 1, 3, 13, 25, 30. 4.10: 1, 5, 9, 12, 13, 15, 16, 23, 31.

Sem4  Ch 4. Written test

Module 5: Integrals

F13     Ch 5.1-5.5. Integrals, definition, fundamental theorem

F14     Ch 5.6-5.7. Substitution

Ö9       Exercises: 5.1: 1, 3, 7, 9, 17, 33. 5.2: 1, 3. 5.3: 1, 5, 9, 11, 17. 5.4: 1, 3, 23.  5.5: 3, 8, 27, 33, 39, 40, 41. 5.6: 5, 6, 7, 9, 21, 23, 43. 5.7: 11, 17.

F15     Ch 6.1-6.2. Techniques of integration

Ö10     Exercises: 6.1: 1, 3, 5, 7, 13, 21. 6.2: 1, 5, 9, 11, 13, 23.

Sem5  Ch 5 and 6.1-6.2. Hand-in

Module 6: Applications of integration

F16     Ch 6.3-6.8, only certain sections. Improper integrals

F17     Ch 7.1-7.2. Applications

Ö11     Exercises: 6.3: 1, 3, 9. 6.5: 1, 3, 5, 15, 23, 33, 34, 35. 7.1: 1, 3, 5, 13, 19, 21.  7.2: 1, 3.

F18     Ch 7.3-7.7, only certain sections. Applications

Ö12     Exercises 7.3: 3, 11, 21. 7.4: 1, 3, 5. 7.6: 1, 7. 7.7: 1, 5.

Sem6 Ch 6 and 7.1-7.2. Written test

Module 7: Curves, Sequences, Series

F19.    Ch 8. Plane curves (not in detail). Ch 9. Sequences and series.

F20.    Ch 9. Sequences and series.

Ö13.    8.1: 1, 3, 5. 8.2: 1, 7. 8.5: 9, 13. 9.1: 1, 3, 17. 9.2: 1, 5. 9.3: 1, 3, 27, 29, 35.

F21.    Repetition.

Ö14.    Repetition. Old exam problems