微信扫一扫
基础课程：数学
Course Name
：
MATH 100 - Differential Calculus with Applications to
Physical Sciences and Engineering
（
UBC
）
Prerequisite:
As a prerequisite to this course, students are required to have a reasonable mastery of
precalculus mathematics (e.g., B.C. Principles of Mathematics 10–12), as this material will
be required throughout the course. This includes being able to
•
evaluate, manipulate, and simplify expressions containing basic mathematical functions,
•
such as polynomial, radical, rational, trigonometric, exponential, logarithmic,
•
absolute-valued, composite, piecewise functions (in particular, in expressions containing
•
powers, exponentials and logarithms, perform algebraic manipulations by applying
•
specific properties of such functions);
•
solve linear, quadratic, rational, radical, trigonometric, exponential, logarithmic, and
•
absolute-valued equations;
•
relate the solutions to the above equations to intersections of graphs;
•
solve linear and quadratic inequalities;
•
find the domain and range of the above functions;
•
construct new functions by applying function composition, identify the various functions
•
that make up a composite function;
•
find intersections of graphs with lines, coordinate axes, and other graphs;
•
write down the equation of a line given two points on the line or one point and the slope,
•
find the slope of a line given its equation, relate the slopes of parallel and perpendicular
•
lines;
•
determine whether a point of given coordinates lies on a certain curve, find the distance
•
between two points;
•
apply Pythagoras theorem, write down trigonometric relationships involving the sides
•
and angles of a right triangle, express proportional relations between similar triangles;
•
compute the area and volume of basic shapes and solids;
•
relate the equation of a quadratic function to the graph of a parabola, and vice versa,
•
and be able to draw the graph of a parabola given the equation;
•
read the value of a function from its graph;
•
for a moving object, compute the average speed over a certain time interval, or use
•
information about the average speed to find the distance travelled or the time elapsed.
新东方前途出国咨询有限公司
Course-level Learning Goals
In this course students will learn the basic ideas, tools and techniques of Differential Calculus
and will use them to solve problems from real-life applications. Specifically, students will
learn.
•
to analyze the behavior of basic mathematical functions (polynomial, radical, rational,
•
trigonometric, inverse trigonometric, exponential, logarithmic, absolute-valued,
•
composite, piecewise functions) both graphically and analytically;
•
to perform differentiation operations and other basic algebraic operations on the above
•
functions and carry out the computation fluently;
•
to recognize when and explain why such operations are possible and/or required;
•
to interpret results and determine if the solutions are reasonable.
•
In addition, students will apply the above skills and knowledge to translate a practical
•
problem involving some real-life application into a mathematical problem and solve it by
•
Means of Calculus. The applications include science and engineering problems involving
•
velocity and acceleration of moving objects, rates of change, exponential growth and decay,
•
Approximations of functions, curve sketching, optimization. In general, when solving a
•
problem students will be able to
•
after reading a problem, correctly state in their own words what the problem is asking
•
in mathematical terms and what information is given that is needed in order to solve
•
the problem;
•
after restating the problem, identify which mathematical techniques and concepts are
•
needed to find the solution;
•
apply those techniques and concepts and correctly perform the necessary algebraic
•
steps to obtain a solution;
•
Interpret results within the problem context and determine if they are reasonable.
•
Students will also learn how to construct simple proofs. They will learn to show that a
•
given mathematical statement is either true or false by constructing a logical explanation
•
(Proof) using appropriate Calculus theorems and properties of functions. In particular, when
•
applying a theorem, students will recognize the importance of satisfying its hypotheses and
•
Drawing logical conclusions.
