Calculus I (Fall 2017) by Ali Sinan Sertöz at Bilkent University

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source: BilkentUniversitesi      2017年9月22日
Calculus I - MATH 101
Limits and continuity. Differentiation and applications (linearization, optimization, curve sketching, l'Hôpital's rule). Integration and applications (areas, volumes, arc lengths, surface areas). Transcendental functions. Integration techniques. Improper integrals.

Lecture 01: Limits I
Lecture 02: Limits II
Lecture 03: One Sided Limits
Lecture 04: Problem on Limits
Lecture 05: Sandwich Theorem
Lecture 06: Continuous Functions
Lecture 07: Intermediate Value Theorem
Lecture 08: Problems
Lecture 09: Derivatives
Lecture 10: Rules of Derivatives
Lecture 11: Problems on Derivatives
Lecture 12: Derivatives of Trigonometric Functions
Lecture 13: Derivatives of Trigonometric Functions
Lecture 14: Chain Rule & Implicit Differentiation
Lecture 15: Problems
Lecture 16: Problems
Lecture 17: Related Rates
Lecture 18: Related Rates
Lecture 19: Linearization
Lecture 20: Minimum & Maximum
Lecture 21: Fermat's Theorem
Lecture 22: Mean Value Theorem
Lecture 23: Problems
Lecture 24: Shapes of a Graph
Lecture 25: Curve Sketching I: Horizontal Asymtotes
Lecture 26: Curve Sketching II: Slant Asymptotes
Lecture 27: Optimization Problems I
Lecture 28: Optimization Problems II
Lecture 29: Optimization Problems III
Lecture 30: Optimization Problems IV
Lecture 31: Newton's Method
Lecture 32: Antiderivatives
Lecture 34: Definite Integrals
Lecture 35: The Fundamental Theorem of Calculus
Lecture 36: Indefinite Integrals
Lecture 37: The Substitution Rule
Lecture 38: Separable Equations
Lecture 39: Areas between Curves
Lecture 40: Areas between Curves
Lecture 41: Volumes by Cylindrical Shells
Lecture 42: The Natural Logarithm Function
Lecture 43: Log & Exponential Functions
Lecture 44: The Exponential Functions
Lecture 45: General Logarithm and Exponentials
Lecture 46: Inverse Trigonometric Functions I
Lecture 47: Inverse Trigonometric Functions II
Lecture 48: L'Hospital's Rule I
Lecture 49: L'Hospital's Rule II
Lecture 50: Integration by Parts
Lecture 51: Trigonometric Integrals
Lecture 52: Trigonometric Substitution
Lecture 53: Partial Fractions Method
Lecture 54: Improper Integrals I
Lecture 55: Improper Integrals II
Lecture 56: Problems