Instructors:
Lecture: Dr J. Pitrik (T 14-16, KF82; Th 10-12 KF87)
Practice: Dr B.Takács, Dr G. Pintér, G. Fehérvári
Presence:
Recommended for lectures, compulsory for practices.
Tests:
Two midterm test.
To qualify for the exam you must earn 40% on both midterm tests.
Examination:
Final examination is written.
Grade:
The final grade is a weighted average based on 20% each of the two midterm tests and 60% of the final exam.
Office Hours:
Dr J. Pitrik: Tuesdays 16-17 (H301) or by appointment via email (pitrik@math.bme.hu)
Other Informations:
http://math.bme.hu/~pitrik/
Weekly Calendar:
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.
http://math.bme.hu/~pitrik/2023_24_1/Calculus1.pdf
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.
http://math.bme.hu/~pitrik/2023_24_1/Calculus2.pdf
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
http://math.bme.hu/~pitrik/2023_24_1/Calculus3.pdf
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
http://math.bme.hu/~pitrik/2023_24_1/Calculus4.pdf
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
http://math.bme.hu/~pitrik/2023_24_1/Calculus5.pdf
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
http://math.bme.hu/~pitrik/2023_24_1/Calculus6.pdf
Week 7, October 17 and 19
Implicit differentiations. Logarithmic differentiations. Derivatives of inverse trigonometric functions. Derivatives of inverse functions.
Book: pp 201-240
http://math.bme.hu/~pitrik/2023_24_1/Calculus7.pdf
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
http://math.bme.hu/~pitrik/2023_24_1/Calculus8.pdf
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
http://math.bme.hu/~pitrik/2023_24_1/Calculus9.pdf
Week 10, November 7 and 9
l’Hospital’s Rule. Growth rates of functions. Graphing functions again.
Book: pp 301-321
http://math.bme.hu/~pitrik/2023_24_1/Calculus_10.pdf
Week 11, November 14 (November 16 is canceled)
Optimization problems, Linear Approximation and Differentials, Newton’s Method
Book: pp 280-300, 312- 321
http://math.bme.hu/~pitrik/2023_24_1/Calculus_10.pdf
Week 12, November 21 and 23
Second Midterm Test, November 27
Week 13, November 28 and 30
