Foundational Math: Calculus, Probability, and Complex Numbers

Are you preparing for a mathematics placement test or an entry exam that requires knowledge of advanced high school topics? Mastering calculus and complex numbers is crucial for success in STEM fields and further academic study. By completing this course, you will possess a solid conceptual foundation in differential and integral calculus, understand the principles of probability, and be proficient in manipulating complex numbers. You will develop the problem-solving skills necessary to apply these mathematical tools accurately in academic settings. What you'll learn: * Understand the fundamental definitions and rules of differentiation and integration. * Analyze functions using derivatives to determine critical points, concavity, and curve sketching. * Configure definite and indefinite integrals to calculate areas under curves and solve basic accumulation problems. * Practice calculating probabilities for discrete and continuous events, including conditional probability. * Master the algebra of complex numbers, including Cartesian and polar forms, and using De Moivre's theorem. * Apply calculus techniques to solve optimization and rate-of-change problems common in standardized testing. The course begins with foundational concepts in calculus, moving systematically through differentiation and integration before introducing the principles of probability theory. The final sections focus on the structure and operations of complex numbers, supported by numerous practice problems and detailed, written explanations. This course is designed for absolute beginners, including high school students preparing for exams or anyone reviewing foundational mathematics before entering university-level study. No prior advanced mathematical knowledge is required. Start building your essential mathematical toolkit today.