calculus
Why?
Calculus is essential for data science as it provides the mathematical foundation for optimization algorithms, machine learning techniques (gradient descent for example depends calculus), and statistical modeling. Understanding rates of change, area calculations, and approximations enables data scientists to develop and implement advanced algorithms.
What?
This course introduces the fundamental concepts of differential and integral calculus. You will learn about limits, continuity, derivatives, integrals, and their applications. The course emphasizes both theoretical understanding and practical problem-solving skills, with applications relevant to data science and computational methods.
Curriculum:
Limits and Continuity
Introduction to the concept of limits, techniques for evaluating limits, continuity of functions, and properties of continuous functions. Understanding these foundational concepts as the basis for differentiation.
Derivatives
Definition of derivatives as rates of change, differentiation rules, applications of derivatives including optimization problems, related rates, and curve sketching. Connection to tangent lines and instantaneous rates of change.
Usual Functions
Study of common functions and their properties, including polynomial, exponential, logarithmic, and trigonometric functions. Focus on their derivatives, integrals, and applications in mathematical modeling.
Integration and Antiderivatives
Introduction to indefinite integrals (antiderivatives), integration techniques including substitution and integration by parts, and applications of definite integrals to calculate area, volume, and other quantities.
Finite Expansions
Taylor and Maclaurin series, polynomial approximations of functions, error estimation in approximations, and applications in numerical methods and computational algorithms.
