# BMETE92AP61

Course data
Course name: Calculus
Neptun ID: BMETE92AP61
Responsible teacher: Máté Matolcsi
Programme: Physicist-Engineer BSC
Course data sheet: BMETE92AP61
Requirements, Informations

## 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.

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