Calculus I: From Real Numbers to Differential Calculus

Learn advanced maths and grow your career in STEM online in weeks

Calculus is more than just numbers – it powers the world around us. Discover how it can help you on this eight-week course from the University of Padova. Master fundamental calc concepts and gain practical problem-solving tools that can be applied in real-world scenarios – setting you up to thrive in the world of STEM.

Get to the root of real numbers and number sequences

You’ll begin by exploring real numbers, their core properties, and how functions define relationships between them. This foundation will prepare you for more advanced concepts like limits and derivatives.

Discover the power of discrete calculus with limits of sequences and series

Building on this foundation, you’ll dive into limits for sequences, setting the stage for limits, continuity and differentiability of functions. You’ll also learn how to use discrete limits to represent infinite sums, a key tool for Probability.

Explore continuity and rates of change

Next, you’ll examine the behaviour of continuous functions and how derivatives describe rates of change. By applying these concepts, you’ll analyse real-world situations like predicting stock market trends or improving supply chain efficiency.

Tackle optimisation challenges

You’ll also use calculus to optimise problems, applying techniques to maximise profits, minimise costs, and allocate resources efficiently. Concepts like monotonicity, convexity, and Newton’s algorithm will be explored through practical examples.

Master asymptotic calculus

By the final week, you’ll explore asymptotic analysis, Taylor and McLaurin formulas. These tools will help you understand the long-term behaviour of functions, crucial for evaluating algorithm efficiency and solving complex problems.

This course is perfect for anyone starting their journey into higher mathematics, especially students studying engineering, physics, computer science, or similar fields.

Whether you’re looking to build a strong foundation in calculus or apply concepts like limits, derivatives, and optimisation to real-world problems, this course will guide you step by step.

While not required, some prior knowledge of algebra and basic trigonometry will be helpful as you work through this intermediate-level course.

This course is perfect for anyone starting their journey into higher mathematics, especially students studying engineering, physics, computer science, or similar fields.

Whether you’re looking to build a strong foundation in calculus or apply concepts like limits, derivatives, and optimisation to real-world problems, this course will guide you step by step.

While not required, some prior knowledge of algebra and basic trigonometry will be helpful as you work through this intermediate-level course.

• Discuss converge and, when possible, value of a sum of infinitely many numbers
• Apply Differential Calculus to provide qualitative plot of the behaviour of a numerical function of real variable
• Model, discuss and solve applied optimization problems, both theoretically and numerically
• Apply asymptotic methods to limits, infinite sums, behaviour of functions.