##
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 (3^{rd} 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**