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The Calculus courses are traditionally divided in two parts: Single Variable Calculus (Calculius 1) and Multivariable Calculus (Calculus 2). Each of the Calculus courses requires certain mathematical maturity. The content of the course depends on specifics of your school. Normally, it includes Differential Calculus and Integral Calculus. Sometimes an Introduction to Differential Equations is included in the course. In any situation a student in Calculus 2 must have a robust knowledge of Calculus 1 and a solid background in College Algebra, Trigonometry and Precalculus. Those who feel not very strong in the prerequisites mentioned above need to have some remedial tutoring. The secret of success is in a persistent step by step training with a lot of home work. No panic attacks. No math anxiety. Solve the problems of gradually increasing difficulty and be successful in each.
A differential equation is a mathematical equation in which an unknown object is a function - in contrast to an algebraic equation where an unknown is constant quantity.
Differential equations are basic mathematical tools in science and technology. Differential and Integral Calculus was discovered by Newton with the main purpose - to solve differential equations which describe the planetary motion, and in more general setting, to create classical mechanics as foundation of Physics.
So, differential equations are a sort of functional equations. A differential equation is stated as a relation between an unknown function and its derivatives (derivatives are results of differentiation of a function - this is where the term “differential” comes from).
Similar to algebraic equations, the methods of solving differential equations significantly depend on the type of the equation.
We need to distinguish several different classes of differential equations: ordinary (with unknown function of one independent variable), partial (with unknown function of several independent variables). Both ordinary (ODE)and partial (PDE) differential equations are classified as linear and nonlinear. Linear equations are classified as homogeneous and non-homogeneous. To solve linear ODE we broadly use methods of Linear Algebra.
ODE are further classified by the order and by the degree. The most important for applications are first-order and second-order ODE. The process and procedure of solving differential equation we frequently call integration. Solving ODE we distinguish general and particular solutions.
Differential Equations make a huge branch of Mathematics.
As prerequisites the full course of ODE requires College Algebra (including Linear Algebra), Calculus 1 and 2.
It involves a lot of interesting application problems from science and technology.
Linear algebra, in general, is a part of mathematics dealing with finite dimensional vector spaces and linear mappings between such spaces. The depth and width of information covered in Linear Algebra courses depend on the level of study: regular High School AP and College level courses of Linear Algebra include discussion of Systems of Linear Equations in several unknowns, naturally represented by formalism of matrices and vectors.
Linear algebra is central to both pure and applied mathematics. For instance Abstract algebra arises by relaxing the axioms leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of this theory. Combined with calculus it allows the solution of linear systems of differential equations. The techniques are also applicable in analytic geometry. It's methods are extensively used in engineering, physics, natural sciences, computer science, and the social sciences (particularly in economics). Nonlinear mathematical models can sometimes be approximated by linear ones. Methods of Linear Algebra are also applied in Statistics,Probability and Operations Research (Management Science)
The study of linear algebra and matrices first emerged from determinants, which were used to solve systems of linear equations. Cramer devised the Cramer's Rule for solving linear systems in 1750. Later, Gauss further developed the theory of solving linear systems by using Gaussian elimination, which was initially listed as an advancement in geodesy. 
The study of matrix algebra first emerged in England in the mid 1800s. Sylvester, in 1848, introduced the term matrix, which is Latin for "womb". While studying compositions linear transformations, Arthur Cayley was lead to define matrix multiplication and inverses. Crucially, Cayley used a single letter to denote a matrix, thus thinking of matrices as an aggregate object. He also realized the connection between matrices and determinants and wrote that "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".
I have solid (20 years) experience in computer programming. MATLAB is my everyday working tool in mathematical modeling related to my current scientific research. I have been teaching several university courses based on development of MATLAB programs (National University, UCSD Extension) for electronic engineers and mathematicians.
Physics is a natural science which subject is the study of matter. Physics studies matter through its attributes like motion through space and time by analyzing related concepts such as position, velocity, acceleration, mass, force, momentum, energy, etc. Part of physics concerned with motion is called Mechanics which includes Kinematics and Dynamics. We distinguish mechanics of material points and mechanics of continuum media (solids, fluids, plazma).We conventionally look at the Universe within different scales and distinguish micro-world (size of atoms and molecules), micro-micro-world(size of subatomic particles), our regular world(size of human body and distances on the Earth surface), marco-world (size of planets and interplanetary distances) and macro-macro world (size of stars, galaxies and interstellar distances). Each of these areas operates within their own time frames and requires specific methods of study, all are joined together by the common laws of Physics. Mathematics plays an extraordinary role in the development of Physics. It would not be an exaggeration to say that the Laws of Nature are written on the Language of Mathematics. Physical variables are incorporated in mathematical equations by the procedures of Measurement. The concepts and methods of measurements, the systems of units of physical variables, are very important in Physics since Physics is both experimental and theoretical science.
Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 16th century, the natural sciences emerged as unique research programs in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences, while opening new avenues of research in areas such as mathematics and philosophy.
Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
In teaching Physics we apply several approaches determined by the intensity and level of Mathematics used in its presentation. Thus, it could be algebra- based or calculus-based course of College Physics. The calculus-based courses are also differ by the use of mathematical apparatus: there are courses where we apply only ordinary differential equations and elementary vector algebra in contrast to other courses where we use partial differential equations, vector analysis and elements of functional analysis. Success in study of Physics is determined by student’s ability to solve problems. The problem solving requires certain skills and techniques which can be obtained only by the appropriate training.
Precalculus includes actually two separate courses: Algebra and Trigonometry. Precalculus prepares students for calculus the same way as pre-algebra prepares students for Algebra I. While pre-algebra teaches students many different fundamental algebra topics, precalculus does not involve calculus, but explores topics that will be applied in calculus. Some precalculus courses might differ with others in terms of the content. For example, an honors level course might spend more time on topics such as conic sections, polar coordinates, vectors, and other topics needed for calculus. A lower level class might focus on topics used in a wider selection of higher mathematical areas, such as matrices and trigonometric functions. I am teaching precalculus and calculus 1 and 2 courses at US Colleges and Universities for more than 20 years and have excellent results in students perfomance in both subjects. I know how to explain complex concepts in a clear and simple form and enable my students to solve precalculus problems with confidence.
Statistics is one of the most important applied mathematical sciences.
I have been teaching Statistics for more than 20 years on different levels - from High School to University level (even for post-graduate students). I worked as a professional Statistician and a Biostatistician in various areas which included Artificial Intelligence, military applications, molecular genetics, sociology, etc.
My approach is based on problem solving technique in a step-by-step manner, supported by clear theoretical explanations. In my teaching of Statistics I use some statistical software like Excel, JMP and other. Sometimes it is sufficient to use simply a graphing calculator TI-83 Plus or above. As a result, my students develop the necessary skills to use this kind of software and become successful in Statistics.