PACKAGE FOR 10 x 2-HOUR SESSIONS OF “CALCULUS 3”
We are offering a 10-session package designed to help students succeed in their Calculus 3 (Multivariable Calculus) courses.
This tutoring program focuses on extending the principles of single-variable calculus into multiple dimensions, with an emphasis on visual understanding, conceptual mastery, and strong problem-solving techniques.
Each session includes:
-Detailed review of class lessons, homework, and advanced problem sets
-Step-by-step guidance on complex multivariable concepts
-Personalized strategies for tackling 3D problems and visualizations
-Regular progress evaluations and customized feedback after each session
-Students will also build key skills such as visualizing higher-dimensional problems, managing time during complex exams, and independently using advanced learning resources to support their academic journey.
Curriculum Overview: (Calculus 3 Topics)
1. Vectors and Geometry of Space
Vectors in 2D and 3D
Dot product and cross product
Lines and planes in space
Cylinders and quadric surfaces
2. Vector-Valued Functions and Motion
Parametric equations for curves in space
Derivatives and integrals of vector functions
Arc length and curvature
Motion in space: velocity, acceleration, and speed
3. Partial Derivatives
Functions of several variables
Limits and continuity in higher dimensions
Partial derivatives and higher-order partials
Tangent planes and linear approximations
Chain rule for multivariable functions
Directional derivatives and the gradient vector
Optimization:
Local extrema
Lagrange multipliers
4. Multiple Integrals
Double integrals over rectangular and general regions
Iterated integrals and Fubini’s Theorem
Triple integrals in Cartesian coordinates
Applications of double and triple integrals (volume, mass, center of mass)
5. Vector Calculus
Line integrals
Green’s Theorem
Surface integrals and Stokes’ Theorem (intro level)
Divergence Theorem (intro level)
By the end of the program, students will have a strong, confident grasp of multivariable calculus concepts and the ability to handle complex 3D and vector-based problems — critical for future success in higher math, physics, and engineering courses.
Additional Notes:
Calculus 3 moves into 3D space — vectors, surfaces, and multivariable functions.
Heavy emphasis on visualization and applications (e.g., optimization, volume, center of mass).
Vector calculus theorems (Green’s, Stokes’, Divergence) may be introduced lightly depending on the course level.
