Mathematics for TEE S2

Chapter 1: Sequences: Arithmetic and Geometric Sequences. Calculating Sums.

Chapter 2: Hyperbolic Functions: Definition, Curves, Derivatives

Chapter 3: Integral Calculus: Integrals, Antiderivatives, the Riemann Integral, Substitution, and First-Order Differential Equations

Chapter 4: Curves and Surfaces: Straight Lines , Planes, Circles, and Parabolas; Cylindrical and Spherical Coordinates; Lengths, Areas, and Volumes of Common Solids

Hourly volumes:

• CM: 18
• TD: 18

The objective of this course unit is to provide the foundational tools needed to solve problems, reason, and perform calculations based on mathematical concepts. This module will cover both a review of existing concepts and the introduction of new mathematical concepts necessary for Earth and Environmental Sciences.

Math Course for TEE, Semester 1

Brief description of the concepts covered in fourth grade:

Chapter 1: Suites

Sequences: methods of generation, arithmetic and geometric sequences, direction of change. Calculating sums.

Chapter 2: Hyperbolic Functions

-Hyperbolic functions: definition, curves, derivatives

Chapter 3: Integral Calculus

• Integral Calculus: Integral of a continuous, positive function over [a,b] as area, antiderivative, antiderivatives of standard functions, example: calculating the Earth’s mass, linearity, positivity, Chasles’ relation, mean value, IPP, example: seismograph signal, change of variables.
• ^First-Order Linear Differential Equations, Example: Carbon-14 Dating, Constant Variation

Chapter 4: Curves and Surfaces

Parametric representation of a line, Cartesian equation of a plane, dot product, normal vector to a line, equation of a circle, parabola of a quadratic polynomial function, cross-sections and intersections (systems, contour lines), cylindrical and spherical coordinates, lengths, areas, and volumes of common solids