This question may be applicable for Academia SE, however this is strictly math-oriented and requires math whizzes' opinions.
I intend to go to a tech institute to get a BS majoring in Computer Engineering and minoring in Physics.
I need to select 1 of 2 tracks in Math for the first 3-4 semesters.
- Semester 1: Calculus & Analytic Geometry 1 + Linear Algebra & Geometry
- Semester 2: Calculus & Analytic Geometry 2
- Semester 3: Calculus & Analytic Geometry 3
- Semester 1: Linear Algebra & Geometry
- Semester 2: Vector Calculus 1
- Semester 3: Vector Calculus 2
- Semester 4: Calculus & Analytic Geometry 3
Regardless of the track I complete, I will go on to further math for the last 4-5 semesters.
Note that Track 1 takes 3 semesters and Track 2 takes 4.
Also, both tracks have Linear Algebra & Geometry; however in Track 1 it is taken in parallel, but in Track 2 it is a prerequisite.
Here are the synopsis of the courses.
Linear Algebra & Geometry: The two main themes throughout the course are vector geometry and linear transformations. Topics from vector geometry include vector arithmetic, dot product, cross product, and representations of lines and planes in three-space. Linear transformations covered include rotations, reflections, shears, and projections. Students study the matrix representations of linear transformations along with their derivations. The curriculum also includes a review of relevant algebra and trigonometry concepts.
Calculus & Analytic Geometry 1: This course introduces the calculus of functions of a single real variable. The main topic include limits, differentiation, and integration. Limits include the graphical and intuitive computation of limits, algebraic properties of limits, and continuity of functions. Differentiation topics include techniques of differentiation, optimization, and applications to graphing. Integration includes Riemann sums, the definite integral, anti-derivatives, and the Fundamental Theorem of Calculus.
Calculus & Analytic Geometry 2: This course builds on the introduction to calculus in Calculus & Analytic Geometry 1. Topics in integration include applications of the integral in physics and geometry and techniques of integration. The course also covers sequences and series of real numbers, power series and Taylor series, and calculus of transcendental functions. Further topics may include a basic introduction in multivariable and vector calculus.
Calculus & Analytic Geometry 3: This course extends the basic ideas of calculus to the context of functions of several variables and vector-valued functions. Topics include partial derivatives, tangent planes, and Lagrange multipliers. The study of curves in two- and three space forces on curvature, torsion, and the TNB-frame. Topics in vector analysis include multiple integrals, vector fields, Green's Theorem, the Divergence Theorem and Stokes' Theorem. Additionally, the course may cover the basics of differential equations.
Vector Calculus 1: This course extends the standard calculus of one-variable functions to multi-variable vector-valued functions. Vector calculus is used in many branches of physics, engineering, and science, with application that include dynamics, fluid mechanics, electromagnetism, and the study of curves and surfaces. Topics covered include limits, continuity, and differentiability of functions of several variables, partial derivatives, extrema of multi-variable functions, vector fields, gradient, divergence, curl, Laplacian, and applications.
Vector Calculus 2: This course is a continuation of Vector Calculus 1. Topics covered include differential operators on vector fields, multiple integrals, line integrals, general change of variable formulas, Jacobi matrix, surface integrals, and various applications. This course also covers the theorems of Green, Gauss, and Stokes.
As a high schooler, I've got not even an inkling of what these terms like "vector calculus", "Stokes' Theorem", "TBN-frame", etc. etc.
So, I've come to ask:
What are the pros and cons of each track, and what is recommended?