Foundational Calculus: Single and Multivariable Functions

Mathematical analysis of functions is the bedrock of advanced science, engineering, and quantitative finance. If you need a deep, rigorous understanding of how variables interact, this course provides the essential foundation. Upon completion, you will possess a solid, formal understanding of single and multivariable calculus, enabling you to approach complex analytical and optimization problems with confidence. What you'll learn: * Understand the rigorous definitions of limits, continuity, and differentiability for functions of one variable. * Master the calculation and application of partial derivatives, directional derivatives, and the multivariable chain rule. * Apply fundamental theorems of calculus to solve definite and indefinite integrals in one dimension. * Learn techniques for optimization in multiple dimensions, including using the Hessian matrix and Lagrange multipliers. * Practice setting up and solving double and triple integrals using coordinate transformations. * Configure solutions to real-world problems involving rates of change and accumulation across multiple dimensions. The course begins by establishing the rigorous definitions of limits and continuity in one dimension before scaling these concepts to functions of several variables. We then transition into differentiation, optimization, and finally, integration techniques, providing ample written exercises for practice. This course is designed for absolute beginners in mathematical analysis, requiring no prior calculus experience, only basic algebra skills. Begin your journey into foundational mathematical analysis today.