The aim of this course is to introduce the fundamental concepts and techniques of mathematics and to develop the mathematical skills necessary for solving engineering problems.

This course introduces the fundamental concepts of calculus, starting with functions, graphs, and basic notation. Students will learn about limits, including one-sided limits and limits at infinity, as well as asymptotes and continuity. The derivative is explored through tangent lines, differentiation rules, the chain rule, implicit differentiation, and derivatives of inverse, exponential, logarithmic, and inverse trigonometric functions. Applications of derivatives include finding maxima and minima, optimization problems, curve sketching, and resolving indeterminate forms using L’Hospital’s Rule. The course then covers integration, defining definite and indefinite integrals, their properties, and applications such as computing areas between curves. Finally, students will master integration techniques including substitution, partial fraction decomposition, integration by parts, and trigonometric integrals.

Thomas Calculus, 2023, 15th Edition, George B. Thomas, Maurice d. we, Joel Hasse, Pearson. Calculus: Early Transcendentals, 2020, 9th Edition, James Stewart, Cengage, Boston, USA.