Lecture: Dr J. Pitrik (T 14-16, KF82; Th 10-12 KF87)
Practice: Dr B.Takács, Dr G. Pintér, G. Fehérvári
Recommended for lectures, compulsory for practices.
Two midterm test.
To qualify for the exam you must earn 40% on both midterm tests.
Final examination is written.
The final grade is a weighted average based on 20% each of the two midterm tests and 60% of the final exam.
Dr J. Pitrik: Tuesdays 16-17 (H301) or by appointment via email (firstname.lastname@example.org)
The course follows the book W.L. Briggs, L. Cochran, B. Gillet, E. Schulz Calculus: Early Transcendentals (3rd Ed). The page numbers refer to this book.
Week 1, September 5 and 7
Introduction to the course. Review of Functions. Domains and ranges. Linear functions. Symmetry of functions. Periodicity. Transformations of fuctions.
Book: pp 1-27.
Week 2, September 14 (September 12 is canceled)
Composite functions. Inverse functions. Exponential and Logarithmic Functions. Trigonometric Functions and their Inverses.
Book: pp 27-56.
Week 3, September 19 and 21
The idea of limits. Premilinary definitions of limits. One sided and two sided limits. Evaluating limits graphically. Techniques for computing limits. Sqeeze theorem.
Book: pp 56-83
Week 4, September 26 and 28
Infinite limits. Limits at infinity. Asymptotes (horizontal, vertical, slant). Trigonometric limits. Precise definitions of limits.
Book: pp 84-103, 116-130
Week 5, October 3 and 5
Continuity. Continuity on an interval. Bolzano theorem. Intermediate value theorem. Classifying discontinuities (removable, jump, infinite). Introducing the derivative.
Book: pp 104-116, 131- 152
Week 6, October 10 and 12
Rules of differentiation (sum, product, quotient, composite functions). Derivative of trigonometric functions. Equation of tangent line. Derivatives as rates of change.
Book: pp 152-200
Week 7, October 17 and 19
Implicit differentiations. Logarithmic differentiations. Derivatives of inverse trigonometric functions. Derivatives of inverse functions.
Book: pp 201-240
Week 8, October 24 and 26
Maxima and Minima. Applications of the derivatives. Mean value theorems (Rolle, Lagrange, Cauchy). Overview before the first Midterm Test.
Book: pp 241-256
First Midterm Test, October 27
Week 9, October 31 and November 2
First derivative test for monotonicity. Second derivative test for convexity. Graphing functions.
Book: pp 257-280
Week 10, November 7 and 9
l’Hospital’s Rule. Growth rates of functions. Graphing functions again.
Book: pp 301-321
Week 11, November 14 (November 16 is canceled)
Optimization problems, Linear Approximation and Differentials, Newton’s Method
Book: pp 280-300, 312- 321
Week 12, November 21 and 23
Second Midterm Test, November 27
Week 13, November 28 and 30