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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

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