Course Description

Mathematics serves as the foundational language in the fields of Science, Engineering, and Technology. The 'Pre-university Calculus' course offered by DelftX is designed as an introductory-level course ideal for incoming university students. This course aims to bridge the gap between high school and university studies by revisiting five key mathematical areas namely functions, equations, differentiation, integration, and analytic geometry. It prepares students for more advanced calculus studies at the university level by reinforcing necessary definitions and the application of basic mathematical concepts and techniques.

What Students Will Learn

• Comprehend and manipulate various elementary functions such as power functions, roots, polynomials, and trigonometric functions.
• Visualize and solve equations and inequalities involving elementary functions.
• Acquire and apply the concepts of differentiation and integration for basic functions.
• Gain insights into analytic geometry, handling geometric objects like vectors, lines, circles, and curves in the plane.

Prerequisites

This course is tailored for students who have completed high school level mathematics and are looking to cement their foundational knowledge in preparation for university-level calculus.

Course Content

• Review of essential high school mathematics
• Detailed exploration of functions and equations
• Fundamentals of differentiation and integration
• Introduction to analytic geometry
• Interactive exercises to solidify understanding

Who This Course Is For

This course is ideal for students who are about to start their university studies in Science, Engineering, or Technology and need a refresher or a firm grounding in basic mathematical concepts used in calculus.

Real-World Application of Skills

The skills acquired from this course are fundamental to academic success in any science or engineering discipline. Understanding calculus is essential for tackling real-world problems in fields ranging from physics and engineering to economics and ecology. This foundational knowledge facilitates the modeling of dynamic systems, optimizing processes, and solving complex problems that require calculus.

Syllabus

• Module 1: Introduction to Functions
• Module 2: Deep Dive into Equations and Inequalities
• Module 3: Foundations of Differentiation
• Module 4: Basics of Integration
• Module 5: Analytic Geometry
• Module 6: Review and Practice Problems
• Module 7: Preparing for University Calculus
• Final Exam