Calculus

Description

Target audience:

• Undergraduate students in mathematics, engineering, physics, computer science, or economics

• Pre-med or pre-business students taking calculus prerequisites

• Students preparing for standardized exams (GRE, GMAT, MCAT sections requiring calculus)

Join the online sessions over Zoom from anywhere.

 

Coverage: 

Calculus is the language of change — the backbone of science, engineering, and economics. Our college-level tutoring sessions are designed to help students not just solve problems, but truly understand the concepts behind the math. From building a strong foundation in limits and derivatives to mastering multivariable functions and differential equations, we tailor each session to meet your course needs and learning style.

Whether you’re preparing for exams, struggling with complex concepts or aiming to strengthen your foundation for exams or graduate studies, our sessions provide:

• Clear explanations of challenging topics

• Step-by-step problem-solving strategies

• Study tips tailored to your learning style

• Guidance with assignments and exam preparation

Topics covered:

Students will learn the following concepts based on their college course syllabus in Calculus (some of the topics listed below).

• Calculus I (Differential Calculus): Limits, continuity, derivatives, applications of derivatives (rates of change, optimization, related rates)

  • Functions and Models

    • Types of functions: polynomial, rational, exponential, logarithmic, trigonometric, Transformations and graphing. Inverse functions

  • Limits and Continuity

    • Intuitive definition of a limit, Computing limits (algebraic, trigonometric, exponential, logarithmic), One-sided limits, Infinite limits and vertical asymptotes, Continuity and the Intermediate Value Theorem

  • Derivatives

    • Definition of the derivative (limit definition, difference quotient), Rules of differentiation: power, product, quotient, chain rule, Derivatives of trigonometric, exponential, and logarithmic functions, Implicit differentiation, Higher-order derivatives

  • Applications of Derivatives

    • Related rates, Linear approximations and differentials, Extreme values (absolute and relative extrema), Mean Value Theorem and Rolle’s Theorem, Curve sketching: concavity, inflection points, first and second derivative tests, Optimization problems (applied word problems), Motion along a line (velocity, acceleration)

  • Introduction to Integration (end of Calc I in many schools)

    • Antiderivatives, Indefinite integrals, Basic integration rules

• Calculus II (Integral Calculus & Series): Techniques of integration, applications of integrals, infinite series, polar and parametric equations

  • Techniques and Applications of Integration

    • Definite integrals and the Fundamental Theorem of Calculus, Substitution rule, Integration by parts, Trigonometric integrals and substitution, Partial fraction decomposition, Improper integrals

  • Applications of Integrals

    • Area between curves, Volumes (disk/washer method, cylindrical shells), Arc length and surface area of revolution, Work, force, and mass problems (center of mass, hydrostatic pressure, etc.)

  • Sequences and Series

    • Sequences and convergence, Infinite series and convergence tests – nth-term test, comparison tests, ratio/root test, alternating series test, Power series, Taylor and Maclaurin series expansions, Radius and interval of convergence

  • Parametric and Polar Coordinates

    • Parametric equations and calculus (derivatives, arc length, area), Polar coordinates and graphs, Calculus with polar curves (areas, lengths)

Sessions can be planned in 1-2 hour increments based on student needs for grade improvement.

Contact us to schedule group or one-on-one sessions.