Lecture Plan and Lecture Notes
Module 1: Limits and continuity
Lecture 1
Download Lecture 1. Elementary functions. Odd and even functions. The absolute value. Chapter P.
Lecture 2
Download Lecture 2. Limits. The Squeeze Theorem. Chapters 1.1-1.3 and 1.5.
Exercise: Module assignments no. 1-6.
Lecture 3
Download Lecture 3. Continuity. The Intermediate-Value Theorem. Max and min. Chapter 1.4.
Exercise: Module assignments no. 7-13.
Seminar: Quiz and exercises.
Module 2: The Derivative
Lecture 4
Download Lecture 4. Definition of derivative. Tangent line. Differentiable functions are continuous. Chapters 2.1-2.7.
Lecture 5
Download Lecture 5. Linear approximation. The Mean-Value Theorem. Increasing and Decreasing functions. Chapter 2.8.
Exercise: Module assignments no. 1-7.
Lecture 6
Download Lecture 6. Maximum and minimum. Implicit derivative. Chapter 2.9.
Exercise: Module assignments no. 8-13.
Seminar: Quiz and exercises.
Module 3: Transcendental functions
Lecture 7
Download Lecture 7. Inverse functions. The exponential function. The natural logarithm. Chapter 3.1-3.4.
Lecture 8
Download Lecture 8. Inverse trigonometric functions. Their derivative. Chapter 3.5.
Exercise: Module assignments no. 1-9.
Lecture 9
Download Lecture 9. Firat-order and Second-order differential equations. Chapter 3.4, 3.7 and 18.6 / 19.6 (depending on the edition).
Exercise: Module assignments no. 10-12.
Seminar: Quiz and exercises.
Module 4: Applications of differentiation and Taylor polynomials
Lecture 10
Download Lecture 10. Applications of differentiation. L'Hopital's rule. Chapter 4.1,4.3, 4.4.
Lecture 11
Download Lecture 11. Linear approximation again. Taylor polynomials. Chapters 4.9-4.10.
Exercise: Module assignments no. 1-6.
Lecture 12
Download Lecture 12. Applications of differentiation, continuation. Chapters 4.5-4.6 and 4.8.
Exercise: Module assignments no. 7-14.
Seminar: Quiz and exercises.
Module 5: Integrals
Lecture 13
Download Lecture 13. Definition of integrals. The fundamental theorem of calculus. Chapter 5.
Lecture 14
Download Lecture 14. The method of substitution. Integration by parts. Chapters 5 and 6.1.
Exercise: Module assignments no. 1-4, 7-8.
Lecture 15
Download Lecture 15. Partial fractions. More examples. Chapter 6.2.
Exercise: Module assignments no. 5-6, 9-12.
Seminar: Quiz and exercises.
Module 6: Applications of integration, arc length
Lecture 16
Download Lecture 16. Generalized integrals. Chapter 6.5.
Lecture 17
Download Lecture 17. Solids of revolution. Volume, arc length and surface area. Chapters 7.1-7.4.
Exercise: Module assignments no. 7-12.
Lecture 18
Download Lecture 18. Parametric curves. Arc length and surface area again. Chapter 8.2, 8.4.
Exercise: Module assignments no. 1-6, 13-17.
Seminar: Quiz and exercises.
Module 7: Series
Lecture 19
Download Lecture 19. Sequences and convergence. Infinite series. Chapter 9.1-9.2.
Lecture 20
Download Lecture 20. More about series. Taylor and Mclaurin series. Chapter 9.3, 9.6.
Exercise: Module assignments no. 1-8.
Lecture 21. Revision.
Exercise: Revision.