After completing this course, students will be able to apply concepts of single-variable functions, limits, derivatives, integrals, transcendental functions, sequences and infinite series, conic section, and the fundamental calculus concepts involving functions of one, two, or three variables to solve applied problems. The topics covered in this course include the real number system, inequalities, function graphs, function operations, trigonometric functions, limits, continuity, derivatives, the chain rule, applications of derivatives, definite integrals, applications of integrals, integration techniques, indeterminate forms, improper integrals, sequences and infinite series, convergence tests of positive series, power series and their operations, Taylor and McLaurin series, conic sections, calculus in polar coordinates, derivatives, limits, and continuity of multivariable functions, directional derivatives and gradients, the chain rule, tangent planes and surface approximations, the Lagrange multiplier method, double integrals in Cartesian and polar coordinates, triple integrals in Cartesian coordinates, and applications of double and triple integrals.

• Explain the concepts of functions and limits (C2).
• Apply the concept of single-variable derivatives (C3).
• Apply the concept of single-variable integrals (C3).
• Apply the concept of sequences and series (C3).
• Apply the concepts of conic sections and polar coordinates (C3).
• Apply the concepts of derivatives and integrals for two and three variables (C3).

1. Introduction

   • Concept of numbers and inequalities
   • Coordinate systems

2. Functions

   • Polynomial functions
   • Logarithmic and exponential functions

3. Limits

   • Limit theorems
   • Limits of trigonometric functions
   • Indeterminate limits

4. Derivatives

   • Derivatives of functions
   • Derivatives of trigonometric, polynomial, logarithmic, and exponential functions
   • Chain rule and implicit differentiation
   • Higher-order derivatives

5. Applications of Derivatives

   • Maximum and minimum
   • Monotonicity and concavity
   • Local extrema
   • Optimization applications

6. Integrals

   • Definite integrals
   • Fundamental theorem of calculus
   • Substitution method

7. Applications of Integrals

   • Calculating area and solid volume
   • Curve length, work, and fluid force
   • Moments and center of mass

8. Integration Techniques

   • Partial integration
   • Trigonometric integrals
   • Rationalizing substitutions
   • Integrals of rational functions
   • Improper integrals

9. Sequences and Infinite Series

   • Positive series tests
   • Power series and operations on power series
   • Taylor and Maclaurin series

10. Conic Sections and Polar Coordinates

    • Parabolas, ellipses, and hyperbolas
    • Axis translation and rotation
    • Parametric curves and polar coordinate systems
    • Polar equation graphs
    • Calculus with polar coordinates

11. Derivatives and Functions of Two or More Variables

    • Partial derivatives and gradients
    • Chain rule and tangent planes
    • Maximum and minimum problems
    • Lagrange multiplier method

12. Multiple Integrals for Two or More Variables

    • Double integrals in polar coordinates
    • Applications of double integrals (e.g., surface area)
    • Triple integrals in Cartesian coordinates

1. D. Varberg, E. J. Purcell, S.E. Rigdon, Kalkulus – Edisi Kesembilan, Jilid
2. Erlangga, 2011. 2. Thomas, Calculus, Thirteenth Edition Volume 2, Erlangga, 2019.
3. H. Anton, I. Bivens, S. Davis, Calculus, John Wiley & Son, 2012