About This Course

Calculus is a foundational course at Astana IT University; it plays an important role in the understanding of science, engineering, economics, and computer science, among other disciplines. This Calculus course covers differentiation and integration of functions of one and multiple variables, with applications. Topics include:

• Concepts of Function, Limits and Continuity
• Differentiation Rules, Applications, Rates, Approximations, and Extremum Problems
• Definite and Indefinite Integration
• The Fundamental Theorem of Calculus
• Applications to Geometry: Area, Volume, and Arc Length
• Techniques of Integration
• Approximation of Definite Integrals, Improper Integrals, and L'Hôspital's Rule
• Multivariable functions, scalar field
• Gradient and its properties
• Applications
• Double and concept of multidimensional integrals

Course goal(s)

After completing this course, students should have developed a clear understanding of the fundamental concepts of single and multivariable variable calculus and a range of skills allowing them to work effectively with the concepts. The main goal is to be able to apply above-mentioned tools to problems in postrequisites courses.

Course objectives

After completing this course, students should demonstrate competency in the following skills:

• Use both the limit definition and rules of differentiation to differentiate functions.
• Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.
• Apply differentiation to solve applied max/min problems.
• Apply differentiation to solve related rates problems.
• Evaluate integrals by using the Fundamental Theorem of Calculus.
• Evaluate integrals using substitution and integration by parts.
• Use L'Hospital's rule to evaluate certain indefinite forms.
• Determine convergence/divergence of improper integrals and evaluate convergent improper integrals.
• Compute the gradient of the multidimensional function.
• Evaluate elementary double integrals and apply them to compute areas and volumes.