MATH 2211 - Calculus I
Personal notes written throughout the semester covering the topics and problems found with Calculus I. If you have an questions, comments, or notice any type of errors, please feel free to contact me.
Chapter 2: Limits
Section 2.1:
Approximating the slope of the tangent line using the slope of a secant line.
Section 2.2:
Limits, when limits fail to exist, and vertical asymptotes.
Section 2.3:
Limits Laws and Squeeze Theorem
Section 2.5:
Continuity, discontinuities, properties of continuous functions, and Intermediate Value Theorem. Includes background information on trigonometric functions, exponentials, logarithmic functions, and equations involving them.
Section 2.6:
Horizontal asymptotes and limits at infinity.
Section 2.7-8:
Applications involving finding the slope of the tangent line and instantaneous velocity, and the limit definition of the derivative. Also looks at spots where a function can fail to be differentiable.
Exam Review:
Includes all important theorems, definitions, and practice problems for sections covered above.
Solutions:
Solutions to the above practice problems.
Chapter 3: Derivative
Section 3.1 - 2:
Power rule, quotient rule, and product rule.
Section 3.3:
Trigonometric derivatives, special limits, and review of plane trigonometry that is relevant to the course.
Section 3.4:
Chain rule
Section 3.5:
Implicit differentiation
Section 3.6:
Derivatives for the inverse trigonometric functions and the logarithmic functions. We also look at logarithmic differentiation and log properties.
Section 3.7-9:
Applications involving physics, exponential growth/decay, and related rates.
Exam Review:
Includes all important theorems, definitions, and practice problems for sections covered above.
Solutions:
Solutions to the above practice problems.